His mother, Judy, the former Scotland national coach, would like him to change his style. But only as far as his mop of hair is concerned. Judy is not looking to Beckhamise him in any way, though. "I just want it to be tidy," she said.
In common with many of the i-Pod generation, however, the 18-year-old Murray is too busy concentrating on his tennis, his music, and his various sporting interests to make the trip to the hairdresser.
He possesses one suit. "I was given it," he says. "I'm not planning to get any more." He would like to drive, "but I don't want a flash car, just something that would enable me to stop using the Tube. I'm not the type that's into flash cars and huge houses."
Then again he is still at the wide-eyed beginning of a career that promises much in the future, when his tastes may develop along with his bank balance.
Having raised his world ranking to No 72 after promising debuts at Queen's, Wimbledon, the US Open and his first ATP Tour final in Bangkok against the great Roger Federer, Murray performed a minor stocktaking exercise yesterday. Such is the media demand for his time that his agents, Octagon, held a press day for him at their Fulham, west London, headquarters.
Murray's fascination with boxing has taught him to keep his guard up at all times, especially if the press is in the opposite corner. At the same time, he is learning the importance of building a relationship with those who write and commentate on him.
One of his advisers, in an ad hoc fashion, is Tim Henman, the reigning British No 1, whose four Wimbledon semi-finals, plus last-four appearances at the French Open and the US Open and a victory at the Paris Masters, have not spared him from the label of a nearly man.
"I've never had more than a 10-minute talk with Tim," Murray says, "but we have spoken about dealing with the press. What he said [about the press] wasn't actually bad. He told me to try not to say anything bad. He told me to take the rough with the smooth and said that even though the British press has been tough on him they have also helped him.
"It's mainly just around Wimbledon time that some people seem to regard Tim as a failure just because he hasn't won Wimbledon. Without him British tennis would have had nothing. Fortunately, he's a strong person and has put up with it for so many years. But the point is that tennis is not just about one tournament."
Asked about his prospects of overtaking Henman, currently ranked 27th, Murray said: "He's still a long way ahead of me. Who knows? He may retire before I get a chance to overtake him. He's still got a good two years left in him."
Does he anticipate that the expectation will shift on to his own shoulders in the years to come? Murray said: "I'm sure it will be on me. Everybody wants a Wimbledon winner for Britain, although grass is not my best surface. I prefer the US Open. Wimbledon's not the only tournament in the world."
Since returning from a Challenger tournament in Mons, Belgium, last week, Murray has taken the opportunity to watch a tape of his Bangkok final against Federer. "That's when I realised how well I've done this year," he said. "Only a few months ago I was watching Federer on television and wondering how I would do against him. But when I watched my match against him I could see a number of things I need to improve.
"I found [Federer] very friendly for someone who's had so much success. He's so talented. He doesn't have to do four hours on the courts, but he still works hard. And his shots are wonderful, with lots of spin.
"Then again, I'd be a bit disappointed if I didn't see four or five things I could improve. Otherwise I'd stay ranked at 72. But what I've seen stays between me and my coach."
Murray, who has not had an opportunity to return to his home town of Dunblane since his adventures on the Tour began, remains fairly anonymous at the moment. "Here in London I just seem to be recognised by 13-year-olds and 17-year-olds, who shake my hand and ask me to sign an autograph."
That number is likely to multiply by the week.
Murray will meet his Davis Cup doubles partner, Greg Rusedski, in singles action next month as Scotland take on England in the inaugural Aberdeen Cup. The event was announced yesterday and will be staged at the Aberdeen Exhibition and Conference Centre on 26-27 November.
Rusedski eased into the second round of the Kremlin Cup yesterday with a straight-sets win over Michael Llodra. The world No 29 overpowered his French opponent at the Moscow event, winning 6-3, 6-1.
It was Rusedski's first competitive singles match since being ousted by James Blake in the first round of the US Open in August. Rusedski will next face either another Frenchman, Fabrice Santoro, or the Russian wild card Igor Kunitsyn.Reuse content