Huw Jenkins has a wry smile at the question, which he must have known was coming when the conversation turns to Cardiff City. Has he ever thought about changing the colour of Swansea City's kit? "No, I think things like that are the basis of what clubs are about," the Swansea chairman says. "Some things need to change, we all need to modernise in football, but I think some things are what our history is about and we've got to keep them."

Agreeing with the enemy is not exactly the done thing in south Wales, especially on the eve of a derby match, but plenty of Cardiff supporters will be nodding at Jenkins's comments and wishing that Vincent Tan, the club's eccentric owner who ended 100 years of tradition by changing their kit from blue to red, shared the views of the man who has been the driving force behind Swansea's renaissance over the past decade.

Jenkins will meet Tan for the first time on Sunday, when Swansea travel to Cardiff City Stadium for the inaugural top-flight fixture between the Welsh rivals. Forty miles on the M4 and two points in the Premier League separate the clubs. Yet when it comes to how the two clubs are run – Swansea carry no debt and have lifelong fans on the board, including an elected member of the supporters' trust; Cardiff have a Malaysian owner who has invested heavily but showed no regard for tradition or the opinions of those that follow the team – they are poles apart.

"I agree," Jenkins says. "I think we are unique the way we run our club. I think with Cardiff, they found an investor to come in and that, at the time, was right for them. I think we've all learned as football supporters, when you've got more often than not one owner, or a group of owners, that have very little attachment or affinity to the club, now and again you are going to have problems. But I think it's up to the supporters to stand as one and they hold the key to sorting it all out.

"I think that's what happened here [when Tony Petty was forced out as chairman in 2002], although it was in a small way [in comparison]. Over the years we've seen a lot of things go wrong at our club, when we were run poorly and we just accepted it. There was a time – and I think it was a great thing – that finally our supporters decided enough was enough: 'We are going to do something about it.' I think no club – Cardiff included – should underestimate what the voice of the supporters can do."

While Tan openly admits he struggles to understand the enmity between Swansea and Cardiff, Jenkins knows as well as anyone what Sunday's game means to supporters. Born and raised in Skewen, a village on the outskirts of Swansea, the 52-year-old watched his first game at the Vetch Field, the club's former home, at the age of four. A fan of the club ever since and chairman for 11 years, Jenkins has seen the good, the bad and the ugly when it comes to derby matches. He is confident, though, that the dark days, when both clubs languished in the lower leagues and violence overshadowed the football, belong to the past.

"I think things have moved on a lot from years ago, because we were always two clubs struggling. I think you had more animosity then," he says. "To be fair, Cardiff got up to the Championship a few years ago and then we followed them and ended up getting promotion first to the Premier League, which was a big thing for us. I think that took away a bit of that competitiveness, because the small-mindedness of trying to compete with Cardiff, and being only focused on them, is something that doesn't register with me. Yes, we want to win the games against Cardiff and I want to win those more than any games, but you can't lose focus."

One thing is clear with Jenkins: he is not afraid to speak his mind, even if he ruffles a few feathers in the process. A question about what the next step is for a club that has climbed from the depths of the Football League to claim a top-10 finish in the Premier League and a first major trophy in their history in the space of 10 years prompts the frank admission that players and staff at the Liberty Stadium need to change their mentality and stop being so defeatist about their prospects against bigger clubs.

Michael Laudrup's side are holding their own in the Premier League and on course to reach the knockout stages of the Europa League but they have collected only one point from home matches against Manchester United, Liverpool and Arsenal and an away game at Tottenham Hotspur. Jenkins is not impressed.

"The biggest thing you need – I've been thinking about this for the last month – and I think we [the board] have got it as people who have been with the club for a long time, is belief that you can compete, because we've encountered reasons why we couldn't compete right throughout each division we were in," he says. "We have to make sure whoever comes in to manage, coach and play for us in the future, they can't be talking about different levels of leagues within a league. To me, that is complete failure.

"When I hear some of our players and staff talking [about getting to 40 points] now it really upsets me that they can actually think like that, because you are more or less conceding a third of the games you play in before you start. I find that the hardest thing to take, that we have actually got staff and players that struggle at this point in time to see where we can compete. And that's the biggest challenge I've got, to make sure that turns around and that everybody working with the club believes if we keep doing things differently, we can compete, irrespective of the size of the club or budgets."

It is a theme that Jenkins returns to time and again without being able to put his finger on the reasons for the change in mindset. "I don't know [why it has happened]. But I've sensed it this season more than ever. We generally tend to talk about things, for me, in the wrong way. We don't see every game as a winnable game, which is not right and it's not our mentality."

By Jenkins' own admission, it was not the easiest close-season at Swansea. At one point it looked like Laudrup might leave as a result of the club falling out with his agent, Bayram Tutumlu. Jenkins says it "never came across to me" that Laudrup could quit and insists his relationship with the manager is no different now to what it was before. As for Tutumlu, Jenkins explains: "The club needed to be back in control of making all the decisions connected to players that come in and out of our club. It's as simple as that."

Shrewd player recruitment has been one of the key components of Swansea's success under Jenkins – players such as Michu, Michel Vorm and Ashley Williams were picked up for next to nothing – but this summer the club released the purse strings and paid £12m for Wilfried Bony. Most chairmen would talk about an eight-figure transfer as a statement of the club's ambition but, typically, Jenkins has a different take.

"It's not what we are about as a club," he says. "Just going out and signing a player that scores 33 goals in Holland, anybody can do that. Just pick the paper up every weekend and there's your top goalscorer. I think our strength is to find players who are not quite tipping the mark somewhere else and making sure that, when they get consistency and a proper structure of playing, they come here and do well. We can't lose sight that's where we've built our club from."

Those foundations remain solid. Despite spending £20m on new players this summer, Jenkins says that wages represent close to 50% of turnover, which is way below the Premier League average of 72%. Attractive to watch on the pitch and well run off it, Swansea's model is widely viewed as the blueprint for clubs across all levels to follow, even if the signing-in book remains blank. "Nobody has come to visit us, ever," Jenkins says. "I suppose it does surprise you a little bit. But there's not much to see, is there?"