After a disappointing Saturday afternoon, at least the funders of one of those aeroplanes hired to fly over The Hawthorns might have been pleased by news emerging from Germany the following day, as it was claimed that Arsenal had made Thomas Tuchel an offer to succeed Arsène Wenger.

Even if the Bild story has been flatly denied by Arsenal and seems like a deal highly unlikely to come to fruition right now, the Borussia Dortmund coach’s name is beginning to be more and more consistently linked with the Gunners. It’s viewed by many as a good fit on an ideological level – and the speculation is being kept alive by Tuchel’s current situation at Signal Iduna Park, where talks on his future are planned with CEO Hans-Joachim Watzke for the end of the season, even though he has a year more to run on his contract.

Whether he would be a good fit for Arsenal’s eventual next step is simply a question of perspective. “He is a very special coach,” said Mario Götze back in January, going on to expand that the former Mainz man’s way of working was “something I have never seen before”. Having made his name – like Jürgen Klopp – at Mainz, some have not been slow to make comparisons between the two. In fact it was the club’s long-serving sporting director Christian Heidel (now at Schalke) who was one of the first to make the link. In a 2010 interview with Die Zeit, Heidel described his then-newly appointed coach as “a loyal and authentic guy, a positive and crazy man, like Jürgen Klopp. I’d have problems with a coach in a suit on the touchline. That’s not what Mainz is about.”

Any semblance of similarity has fallen away since Tuchel again followed in Klopp’s footsteps by joining Dortmund, where he began work on July 2015. The sharp differences in their most recent incarnations were widely welcomed at first. Having become a tired, one-trick pony under Klopp, BVB were transformed under Tuchel into a tactically versatile beast that could counterattack in their familiar style or force the play, and which knew both when to press and when was the moment to sit off and conserve energy. They were good to watch again, but durable and practical too. So he knows plenty about refreshing a tired team that’s become stuck in a rut.

The turnaround in individuals was particularly striking. Mats Hummels, coming off a tricky season in which Klopp had been forced to publicly defend his media criticism, started to look like one of the Bundesliga’s best defenders again. Ilkay Gündogan, having struggled badly for form and fitness, had only really stayed because Dortmund had failed to garner any serious offers for him – now, he was back to running the midfield.

Perhaps most impressively of all, Henrikh Mkhitaryan – who had rarely looked like justifying the club record outlay of €27.5m to Shakhtar Donetsk in 2013 in two indifferent seasons – was as lively, dangerous and explosive a deep-lying attacker as you could imagine, dovetailing perfectly with the even-more rapid Pierre-Emerick Aubameyang. It did not go unnoticed that Tuchel had presented Mkhitaryan with a copy of The Inner Game of Tennis by Timothy Gallwey in pre-season training, which is about visualisation and clarity of thought. Whether it was solely down to the book or not the coach had got into his, and so many of his team-mates’ heads.

Some will take Tuchel’s failure to make Dortmund a genuine title rival to Bayern Munich this season as evidence that he is not yet ready for a challenge at one of the Premier League’s elite, but he simply became the victim of his own success. His regeneration of that star trio meant that they were all sold, each with a year left on their respective contracts, leaving him with the unenviable task of meeting increased expectation without the spine that had served him so well in the previous season. At the same time he has had to adapt a young squad which has been subject to wholesale turnover to his needs, with very little time in which to do so.

At least, were he in north London, you feel he would be judged on his own merits. Dortmund is a club – and a brand – that’s big on emotion and the concept of “feeling”, and the growing sense is that there’s precious little of it between club and coach. Even in the glorious first flushes of his debut season, there were fans who missed Klopp’s bluster and warmth, suggesting that Tuchel was more about the head than the heart – although those who saw the latter expressing his excitement over Barcelona’s comeback against Paris Saint-Germain in an interview with Jan Aage Fjortoft after the Champions League win over Benfica will know how passionate he is about the game, albeit in a far less bombastic way than his predecessor.

The dissenting voices, though, have become more pronounced with this season’s inconsistencies. The former Dortmund defender Michael Schulz complained to Sky earlier this year that “Thomas Tuchel is not Klopp” before claiming “he doesn’t really fit this club”. Regardless of the myriad challenges Tuchel would face were he to eventually replace Wenger, the unrest of recent weeks suggests that him not being enough like the long-serving Frenchman is unlikely to be one of them.

In that 2010 Die Zeit interview, Heidel had praised Tuchel’s ability to relate. “He has something that distinguishes the good from the very good coaches,” he said. “]He has] social skills in dealing with and communicating with the players.” That hasn’t always extended to those around him of late, his relationship with the influential head of scouting Sven Mislintat deteriorating, apparently over the Götze deal, and the clear signals that Watzke and sporting director Michael Zorc are increasingly steering transfer policy without him. Tuchel is not loud, but he is assertive.

Even if an eventual Tuchel arrival at Arsenal might not quite be the culture shock of, say, Diego Simeone coming in, it would be revolutionary for the Emirates Stadium in its own way, in introducing a tactical micro-manager with a new energy. It seems that now is not the moment. The question is whether Tuchel will have further time at the Westfalenstadion next season to perfect his command of coaching, and management, at Champions League level.

Talking points

• At the current rate, Anthony Modeste won’t be able to live up to his name much longer (sorry). His hat-trick for Köln on Saturday – including a first two within 120 first-half seconds of each other – took his team to a rousing 4-2 win over Hertha Berlin and into the Europa League spots. It also took him above Robert Lewandowski in the Bundesliga scoring charts and just one behind table leader Pierre-Emerick Aubameyang. The Frenchman has now struck 22 times, and Köln are mightily pleased they refused a mind-boggling €50m offer for him from Tianjin Quanjian last month – they were so keen to hang on to Modeste that sporting director Jörg Schmadtke personally called the Chinese Super League club’s coach Fabio Cannavaro to ask his club to stop their “disrespectful and aggressive” approaches. There’s still the sense that Modeste is just a good player having an exceptional run of form, but there’s no arguing with his dead eye in front of goal this season. Not bad for a player who managed more red cards than goals (one versus zero) in six miserable months on loan at Blackburn in 2012.

• Failed strop of the week goes to Arjen Robben, whose petulant waving away of Carlo Ancelotti’s greeting when he was substituted near the end of Bayern Munich’s win at Borussia Mönchengladbach was the subject of much hilarity on the visitors’ bench. It was eventually down to everybody’s favourite dad figure, Xabi Alonso, to give Robben a consoling pat on the leg as he threw a plastic bottle in frustration. That this was an anecdote rather than a point of polemic tells you exactly where Bayern are at the moment – happy, relaxed, and cruising. They’re 13 points clear at the top after a 17th win in their current 19-match unbeaten run (all competitions) and hey, Thomas Müller even scored the winner, his second Bundesliga goal of a curious season. It capped a pretty deflating week for Gladbach after they fell victim to a stirring Schalke comeback in the Europa League on Thursday. Die Königsblauen, meanwhile, kept the good vibes going (and leapfrogged Gladbach) by winning 1-0 at Mainz through a Sead Kolasinac goal.

• After five straight defeats, Eintracht Frankfurt stopped the slide with a goalless draw against Hamburg – perhaps predictably given their opponents. HSV have now not beaten Eintracht in 10 attempts, and weren’t helped here by referee Benjamin Kortus missing what should have been a clear penalty for David Abraham’s second-half foul on Filip Kostic. The real reason for joy, though, was Marco Russ’s return to the Eintracht starting XI for the first time since recovering from cancer that was discovered last May, with coach Niko Kovac bringing him into a three-man backline. “He asked me how I felt, and I told him that I had to be thrown in at the deep end at some point,” Russ said after the match, in which he gave a solid performance in his 80 minutes on the pitch. Rarely has a clean sheet been such cause for celebration.

• It would be ridiculous to say RB Leipzig are in freefall – they’re still second – but Saturday’s 3-0 slump at improving Werder Bremen was a fourth loss in seven matches, started by Zlatko Junuzovic’s blockbuster from outside the area. They haven’t changed much in that time (even if the switch to three at the back at Weserstadion wasn’t exactly a resounding success) and it was easy to have sympathy for Ralph Hasenhüttl’s view that his team were simply having “less luck than in the Hinrunde”. To his credit, the Austrian also said his team “aren’t doing enough” but they have a chance to rectify that with a couple of very winnable upcoming fixtures, at home to Darmstady and away at Mainz.

Results: Augsburg 1-1 Freiburg, Borussia Dortmund 1-0 Ingolstadt, Borussia Mönchengladbach 0-1 Bayern Munich, Eintracht Frankfurt 0-0 Hamburg, Hoffenheim 1-0 Bayer Leverkusen, Köln 4-2 Hertha BSC, , Mainz 0-1 FC Schalke, Werder Bremen 3-0 RB Leipzig, Wolfsburg 1-0 Darmstadt.