Typical Medvedev answer: 'Well, to tell you the truth, I was wondering whether I could persuade that blonde girl in the front row to come out for dinner with me tonight.'
This remark is delivered in such a way as to suggest that his chances of success would be high. There is a lot of charm there. But there are other things too: a sense of mischief, and a knowingness that carries more than a hint of parody. Medvedev enjoys playing up to the image of the deep and mysterious Russian, whose appeal is danger and whose danger is his appeal.
Tennis has been on the look-out for 'characters' ever since McEnroe and Connors faded from the scene. It found one, of sorts, in Andre Agassi, and in Medvedev there are the makings of another. But any similarity between Andre and Andrei begins and ends with their names.
Whereas Agassi has always seemed the embodiment of an America at its most flashily disposable, Medvedev comes with a quite opposite set of cultural baggage: the brooding product of a troubled land where to be a hero - sporting or otherwise - means carrying the weight of history on your shoulders. And in the case of Medvedev, whose own short life has been far from immune to the turbulence of Russia's recent past, that is truer than most.
It's an aspect of Medvedev that is not lost on his coach, the American Brad Stine. 'I think for us in the West, we always feel that there's something lurking there that we don't quite understand,' he says. 'He has a unique personality, very intelligent, very charismatic, and somebody who could be very good for tennis.'
Medvedev, who will be 20 at the end of August, was born in Kiev in what was then the Soviet Union. But since its break-up he has become a Ukrainian - by birth if not by inclination. His parents are ethnic Russians, and he considers himself Russian, although it is UKR that appears after his name.
Medvedev is one of those former Soviet citizens for whom the political changes of the past three years have left them feeling at best disenchanted, at worst fearful. He hates the idea of finding himself representing Ukraine in a Davis Cup match against Russia.
'I don't share the decision to break up the country,' he once said. 'They call us Ukraine and they want me to be proud that they call me a Ukrainian. But I never will be because my nationality is Russian.' Now his line on the subject is more neutral. 'I don't defend the flag of any country, be it Ukraine or the Soviet Union or America or anywhere else. I just play for myself.'
Politics has not been the only blight on Medvedev's life. His parents were divorced when he and his elder sister Natalia - also a tennis player - were very young, and then in 1986 the family found themselves among the millions threatened by the nuclear fall- out from the Chernobyl disaster which occurred only 60 miles from Kiev. A number of Medvedev's schoolfriends died, and the fear that he might have long-term health problems has remained with him. Only in the past year have Medvedev and his mother and sister been able to move away from the area, finding a home in Stuttgart.
In a life full of upheaval, tennis has remained a constant. Having been introduced to the game by his mother, Svetlana, who now coaches his sister, Medvedev went on to become the Soviet Union champion at three stages of his junior career, turning professional when he was only 16. Since then he has won eight titles and risen to as high as No 4 in the world rankings. He is No 6 at the moment, though his inexperience on grass has inclined Wimbledon to seed him at No 9.
Yevgeny Kafelnikov, the Russian who has started to make his mark this season and is the No 15 seed at Wimbledon, grew up playing tennis with Medvedev. He remembers someone who was always prepared to work hard at his game, much more so than he was himself. Which explains why Medvedev, though younger by a few months than Kafelnikov, got to the top so quickly.
Medvedev's potential to go on improving is what tempted Stine to stop being part of the team of coaches that worked with Jim Courier and take on his first solo coaching role with Medvedev only last month. 'He hadn't won a Grand Slam, and that gave us something to work towards.'
While accepting that Medvedev is primarily a clay- court player, Stine believes that grass could suit him. 'Two of the most important things on grass are serve and return, and I think he does both of those very well. He's got an attacking sort of approach, and I think that also translates well on to grass.' Certainly Wimbledon - where Medvedev was knocked out in the second round on his only previous appearance there last year - satisfies Medvedev's desire to get the points over quickly.
Bulkily built to the point of having to guard against becoming overweight, Medvedev has all the shots to excite a Wimbledon crowd. But his heartfelt approach to the game is where his real appeal lies. When things go wrong - and with a high- risk game like Medvedev's they are bound to do so sometimes - the soulful figure he cuts is especially endearing. But his humour is never suppressed for long and you will find him offering his racket to someone in the crowd with a smile that is like the sun coming out. And perhaps even trying to fix up a dinner date.
Tennis loves a romantic, and it has got one in Medvedev, whose unrequited love for the German player Anke Huber was hot gossip last year. Eventually he won her, and the two of them now live in neighbouring apartments. Not that his eye has stopped wandering, or his imagination. Medvedev talks a lot of nonsense, but it is always very entertaining nonsense, and he has a real gift for comedy.
All this is great fun for tennis fans, but how does his coach feel about it? Mavericks like Medvedev aren't always ideal to work with. Stine, though, believes that self-expression as a person can be good for Medvedev as a player. In any case, he says, if we imagine that Medvedev is too busy looking for girls in the crowd to be able to concentrate on his tennis then we are probably mistaken.
'Actually I think he thinks about tennis quite a lot,' Stine says. 'He's very perceptive in his ideas about the game and in dissecting his own matches. And a lot of players don't want to give away their deepest thoughts about certain situations in matches. Andrei has his own way with dealing with that, and if he can do it humorously then that's great.' The man is a performer, and there is no better stage than Wimbledon.
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