There was a moment, as Thomas Müller sat on the top table at Wembley and looked far too relaxed for a man about to play one of the biggest games of his life, when the expression on his face conveyed the bemusement you might expect if he had just been asked to announce his pin number in the middle of a press conference. In fact, he had just been asked whether Bayern Munich had any weaknesses.

"Weaknesses?" Müller replied. "Maybe that is a question for Dortmund. I don't think we have any weaknesses at all."

Then he thought about it a little longer. He picked out the game at Borussia Mönchengladbach last weekend and he acknowledged that maybe they were not flawless, after all. Bayern, he pointed out, had conceded three goals in that game. What he did not mention was that Jupp Heynckes's team, true to form, had scored four of their own.

That was the 15th time Bayern have managed four or more goals this season. The 14th was against Barcelona when they made Lionel Messi look ordinary, prompting El Mundo to mark their appearance in another final, their third in four years, with the headline "Gran Bayern". If there are weaknesses, they are devilishly hard to find. "We are an extraordinary team," Heynckes said, matter-of-factly. "We have been the best side in 50 years of the Bundesliga and, along the way, we have broken just about every record." Twenty of them, to be precise.

They will certainly be formidable opponents if the Borussia Dortmund story is to get a Hollywood ending. From bucket-collection skint to a Champions League final, Jürgen Klopp likened Dortmund's journey to climbing Mount Everest. Yet he also made the point that not every story has a happy ending. "People have climbed Mount Everest before and had to turn around 10 metres from the top, but at least they've tried. And we've tried too."

Dortmund will be facing a side, to put it into context, that finished 25 points above them in the Bundesliga. Bayern won the title with six games to spare and ended up with 91 points over 34 matches. They scored nine in one match, went four months without conceding an away goal and their goal difference eventually settled at plus 80. Their points total is 10 more than the previous record, set by Dortmund last season, and two more than Manchester United managed in 38 Premier League games.

Yet Dortmund's underdog status should not be overplayed when, to quote Arsène Wenger, they are "rolling onwards like a steamroller." These are not starry-eyed innocents who might suddenly be consumed by anxiety. There is a fearlessness about them that neutrals can only find endearing. Klopp, more than anyone, symbolises it. "It's more than a win-win situation. It's a win-win-win-win situation. If I were looking at it from the outside, I would say: 'Incredible!' But I'm in the middle of it and I don't have time to reflect." He did, however, have time to reflect on the day he became so animated on the touchline he pulled a muscle. His conclusion: he would try to calm down a little next season.

The last time his team played Bayern, he became embroiled in a jarring exchange of views on the touchline with the opposition sporting director, Matthias Sammer, and the arguments spilled over into the media. Perhaps this was why Heynckes began his press conference by saying he hoped for a "peaceful" match.

Relations have hardly been helped by the Mario Götze transfer and the growing sense that Robert Lewandowski will be joining him in Munich later in the summer. For Dortmund, the sad reality is that a team of brilliant potential and spirit might soon be broken up – or, at least, find their momentum stalled – whatever happens at Wembley.

Losing this final threatens to accelerate the process – but, crucially, they do know they can beat Bayern. Their Bundesliga encounters this season were drawn but Dortmund had a couple of 1-0 wins en route to the title a year ago. A 5-2 trouncing in the German Cup final last season – "the most extraordinary performance I have ever seen from a football team," Klopp called it – should also be relatively fresh in the memory.

On the flipside, Bayern eliminated Dortmund on the run that will see them play Stuttgart in the German Cup final next weekend. Heynckes, retiring after 34 years as a coach, talked about this being the most complete Bayern team he had ever seen. It was a side, he said, that had no weaknesses and he used the example of Franck Ribéry to make his point.

"When I arrived, Franck Ribéry played football just one way – always attacking. He is a world-class player, an excellent provider and a great finisher. But he has learned over the past two years that in football you also need to do defensive work. That's why we have conceded so few goals this season."

The same applies to Arjen Robben on the other wing. More than that, Heynckes can cite "Ribéry, Mario Gomez, [Mario] Mandzukic, Müller, [Xherdan] Shaqiri …they have all learned to defend."

A lot of people have questioned the fact Bayern come into this match after losing four of their last five Champions League finals and suggested that somehow it might hold them back. On the contrary, everything about Bayern's buildup has offered the sense they regard it as a form of motivation. They seem affronted by the fact they have won the European Cup only once since that run of three successive triumphs in the mid-1970s. Losing to Chelsea on penalties last season? That, according to Heynckes, has been the driving force this time around. "That was our starting point," he said. "From the first day, you could tell everyone was determined to change things. We improved a few things, we changed a few things. We have been playing fantastic football. And if we can draw on that, we are going to win the match."

His players certainly give the sense of being remarkably relaxed. Müller described it at one point as a "quite normal" match. Philipp Lahm, the captain, was asked for some insight into the day and made it sound like little more than just another run-out on the training ground. "Wake up, breakfast, siesta, coffee and cake, play football and hopefully celebrate."

Just for good measure, Bayern have already booked their party venue, with a 5am licence. Dortmund have their own party booked. The difference, perhaps, is that, whatever the result, Klopp leaves the sense he will be last off the dancefloor anyway. "It's the perfect final, against the perfect opponent, at the perfect stadium. If I die now, it was not so bad."