It all boils down to one thing for Tottenham Hotspur now and it is whether they can go that next, decisive step. Can they turn all that forward momentum and vibrant, often thrilling football into something more serious and memorable or will we will discover it was nice while it lasted but all just a sideshow to the real story of two Manchester clubs rubbing up against one another like sandpaper?

Are their ambitions restricted simply to the Champions League places and finishing above Arsenal for the time in the Arsène Wenger era, or do the Premier League's third-placed team have the wit and gumption to catch and overhaul Manchester City, the world's most financially endowed football club, and actually win the damn thing?

The answer, whenever this is put to Harry Redknapp, is that of course they can, while never straying from the fact that this is a team dramatically playing above expectation. Others will struggle to get past the scepticism that has clung to Spurs down the years and wonder how long the title race can go before they politely show themselves to the door. Redknapp himself seems surprised sometimes. "People keep saying that Manchester United haven't played well. They have 48 points [from 21 games]. God knows what's going to happen when they start playing well. It's frightening."

The trajectory has been so steep it is easy sometimes to forget that when Redknapp began this job, in October 2008, the team he inherited were at the bottom of the league, with two points from their first eight league fixtures. They have 46 from 21 games, which is more than the champions, United, had managed at the corresponding stage last year. Sir Alex Ferguson has been talking about them as title challengers since last summer and, though he has not always been convinced, Roberto Mancini is also now acknowledging the threat may be real and sustained. "They can win the title," Mancini said before Sunday's first-versus-third encounter at the Etihad Stadium. It was the first time he had uttered those words this season.

But it is not straightforward. The backdrop to all this is that on Monday Redknapp will stand trial with Milan Mandaric over charges of cheating the public revenue, which he denies, relating to tax payments when they worked together as manager and chairman at Portsmouth. For two weeks Joe Jordan will take over training, just as he did in November when Redknapp had surgery to unblock coronary arteries. Beyond that, it rests on the verdict of a jury at Southwark crown court.

These are the best of times for Spurs otherwise. Press conferences are full of levity and banter. White Hart Lane, once again, is a happy place to be. In August they lost 5-1 to City but, since then, it does not need a forensic examination of their recovery to understand why Redknapp is so prominently in the Football Association's thoughts when it comes to replacing Fabio Capello after this summer's European Championship.

"I didn't go home that night despondent," Redknapp recalls. "I was disappointed to get beaten like that but it wasn't as though I thought: 'This is my team for the season, we are in trouble here.' I knew we had reinforcements coming in that would make the difference."

Scott Parker arrived from West Ham and slipped seamlessly alongside Aaron Lennon, Rafael van der Vaart, Gareth Bale and Luka Modric into a midfield revered as the best in the country. Emmanuel Adebayor, ostracised under Mancini, has been reinvigorated since joining on loan from City. Maybe above all else, the transfer window clanked shut without Modric leaving for Chelsea. Spurs had been regarded as a selling club for longer than their supporters would care to remember but here was the evidence that they were no longer willing to undermine their own ambitions.

If there is a weakness, it may be that they are a team who need a little bit more knowhow. Spurs have only one player, William Gallas, with a Premier League winner's medal, from his time at Chelsea. City have four, although two of them are Carlos Tevez and Wayne Bridge. United, in contrast, have 21 players with a collective 71 league medals, including 10 who have won it four times or more.

Yet Redknapp has assembled a squad with few flaws. "It's not rocket science. Good players give you a chance and we have good players – Modric, Parker, Van der Vaart, Lennon, Bale; good attacking players. [Kyle] Walker has emerged as a fantastic prospect. The left-back [Benoît Assou-Ekotto] is a good player. [Younès] Kaboul is now the player I thought that he could have been when I took him to Portsmouth. And I might be knocking my own job here – but if I haven't got Bale, I am not half as clever, am I?"

All of this has been done, as Redknapp is fond of pointing out, with a clear disparity between his own net spend, £18.4m, and Mancini's, £190.5m. "It's a different game when you buy players and pay them £250,000 a week," he says, tongue in cheek. "To be honest, I'd fancy you [journalists] to manage [them]. You'd have a chance, wouldn't you? You'd win the league."

If that sounds slightly derisory of Mancini and City it is not the first time Redknapp has taken this line. "We have not done it the easy way," he said last week. "Spurs are not third in the Premier League because someone has walked through the door at White Hart Lane and slapped a bundle of money on my desk."

Sergio Agüero was used as an example in his latest offerings. "Anyone could have looked at him when he was in Spain and said: 'I would like him in my team.' It wasn't difficult to do, really. It was just whether you had £40m and could pay him £250,000 to £300,000 a week. That was the only stumbling block."

Mancini applied some gentle humour when he was notified of Redknapp's claims. "He can borrow money from us if he doesn't have any," the Italian said. There is, however, a degree of indignation. Spurs, in truth, have spent £238m over the past five years, or a net £76.2m, higher than every club bar City, Chelsea and Liverpool. "They have bought good players," Mancini says. "Maybe not like us in the last two years but over a longer amount of time."

At Arsenal, one of the more revealing moments came at one of Wenger's recent press conferences when he was asked one too many questions about their north- London rivals. Wenger did not take kindly to being drilled for his thoughts about the title chances at White Hart Lane. His voice picked up speed, as it always does when something has got under his skin. "We are in an Arsenal press conference," he pointed out tersely.

Spurs have not finished ahead of their rivals since 1995, when the clubs were seventh and 12th. They currently have a 10-point lead and a goal difference that is superior by 11. The question for Redknapp and everyone at Tottenham is whether this should be the limit of their ambitions and very soon we will have the answer.