The young man with the big smile sitting facing me is the official World Footballer of the Year. He looks more like an Edwardian poet.

Willowy and fat-free, brown hair shiny as in a shampoo advert, with white middle-class skin that reveals he has never eaten a duff meal in his life, Kaká could be the Brazilian Rupert Brooke.

His club, AC Milan, are reigning European and world club champions, and on Wednesday they visit Arsenal in the last 16 of the Champions League.

Does he have moments on the field when he feels “what I’m doing now is perfect”? “Yes,” replies Kaká, 25, in his American-tinged English. “Sometimes, everything that I want to do I can do. These are good games, a perfect game.”

When has he felt like that? “Ah, against Manchester [United], the semi-final of the Champions League. Both games, I could do everything that I thought.” Was there any particular moment of perfection? “The second goal in Old Trafford.”

Phil, AC Milan’s English teacher, sitting in on his pupil, recalls the scene: Kaká somehow contrives to get two of United’s defenders to bump into each other and fall over. What’s startling is his composure: he runs with his head up, seeing everything and, when it’s time, gently slots the ball past the keeper.

We are at Milanello, Milan’s training ground in the Lombardian countryside near Lake Como, which may be the world’s nicest office. The air is so clear here that, at 10 yards, you can see the pores in a man’s skin. The six training fields are so flat that you can lie on the ground and not see a single undulation. You sit in the bar, drinking perfect espressos for free, and every young man who passes, world champion or not, says, “buongiorno”.

The players here are kept perfect by football’s best medical team. Just in case the Milan Lab, as the centre is known, needed any more oomph, last week it took Microsoft as a partner.

Before meeting Kaká, I asked the club’s doctors about him. Jean Pierre Meersseman, head of the Lab, shrugged: “What can you say? He’s number one. Nobody is faster than him, nobody has the acceleration he has.”

Daniele Tognaccini, chief athletics coach, dubbed Kaká “the kilometres man”. Though the Brazilian is a creator, he also covers more turf per match than any team-mate except midfield workhorse Rino Gattuso.  

Kaká has arrived only 20 minutes late for our meeting, which for a footballer is early. He apologises for having missed me yesterday, has a stand-up read of the Gazzetta dello Sport newspaper, and then ponders the question of whether it’s fun being Kaká. “It’s a lot of pressure, responsibility. But these are good things: to have a big responsibility with Milan, it’s good. I can manage this pressure.”

But when the season ends, can he finally relax? “I just relax when we win something. If we lose something, it’s difficult to relax.”

Kaká joined Milan in 2003. Uniquely in football, the team has barely changed since then. Have his colleagues here at Milanello become more than just colleagues? “Milan is a big family. In the year, I think, the same time I spend with my wife I spend here with my friends. The day before the game, we stay here in training camp. If we got 60 games in the whole season, there’s another 60 days in camp, and every day training.”

The “feeling” between him and his fellow midfielders, he says, “is abnormal”, adding: “We’ve been playing together for five years and now I know how Gattuso moves, [Andrea] Pirlo, [Clarence] Seedorf. We can play without seeing each other.”

But is it hard to get motivated for 60 games a season? “Sometimes it’s too much,” Kaká agrees. “Every time we play in Champions League, we always have motivation and concentration. Champions League is always important because you have to win, every game. Championship – you have to win every game but sometimes you don’t have the motivation that you have against Inter, Juventus, Rome and Champions League games.”

He is presumably referring to games in half-full stadiums in provincial Italian towns with hooligans chucking things. Is that why Milan are only fifth in the Italian championship? “Errm yeah, I think,” and he gives an embarrassed chuckle.

The question of motivation preoccupies Kaká. When he arrived at Milanello, he says, he noticed a curious quality about Paolo Maldini, Milan’s renowned defender: every day, the guy wanted to win. “This surprised me,” says Kaká. “For that I learn everything about Paolo. Why he’s got this motivation, and the other players don’t.”

It may explain why Maldini at 39 is in his 23rd (and final) season in the first team.

Kaká once thought of doing an MBA. Like many corporate types, he motivates himself by setting himself objectives. But what objectives can he possibly have now that he has won everything? His habitual grin grows to cover the whole porcelain face.

“I want to win everything again. World Cup and Champions League, championship and Golden Ball, World Fifa player of the year and” – he trails off, possibly because the list is endless. “These are the things I learned with Paolo. Always win.”