Andy Murray, who has became the first British man to reach No3 in the world, has been tipped to become a Grand Slam champion by the end of the year.

Murray has 11 tour titles but Greg Rusedski, who like fellow British star Tim Henman made it to fourth in the rankings, thinks the Scot can break into the exclusive Grand Slam-winning club at either Wimbledon or the US Open.

Should Murray do that then he will strengthen his chances of overtaking the second-best player in the world, Roger Federer, who he now trails by 1180 points.

Rusedski said: “It is a wonderful achievement to reach No3 in the world.

“Tim and I managed to get to No4 and in my case, injury meant I couldn't try to get any higher and I don't think people really understand how difficult moving up just one place can be when you are already inside the top five.

“It is similar to someone who is No100 putting together a run of results and finally breaking into the top 20.

“That is the size of the leap in terms of work needed and success on court to ensure you move up just one place at the top of the game.

“Significantly, this also puts Andy one step nearer the No1 position Rafael Nadal holds and given Andy's consistency this year and the success he has enjoyed on court, I don't see any reason when he cannot finish the year in second place.

“To reach the top, Andy is going to have to win a Grand Slam title and that could come this year at Wimbledon or the US Open.

“I have no doubts that if Andy doesn't win that first Slam in 2009 it will come in the next two years and once he gets that debut title, more will come.”

Rusedski finished runner-up at the US Open in 1998 and Murray matched that achievement last season.

Despite losing a one-sided final to Federer, Murray did prove in New York he has the mental strength to go deep into a Slam tournament, beating Nadal in the semi-final.

The British No1's next bid for a Grand Slam title comes at the French Open in a fortnight.

Unfortunately, clay is Murray's least favourite surface and despite reaching the semi-finals of the Monte Carlo Masters last month he lost to qualifier Juan Monaco in his opening match in Rome a week later.

With the US Open and Australian Open played on hard courts that perfectly suit Murray's game and his ability to handle the vagaries of Wimbledon's grass courts, the Scot is equipped to be a Slam winner.

Rusedski believes the fact Murray has got so high in the rankings withoutwinning one of the big four tournaments should be applauded.

He said: “I know some critics will say how can Andy be considered a potential No1 or No2 in the world when he hasn't won a Grand Slam yet and Rafa has six and Roger Federer is there with 13.

Chile's Marcelo Rios is the only player in the modern era to have been No1 and not to have won a Slam and that highlights just how hard it is to claim the top spot without clinching a major title.

“In the women's section, there are players who have made No1 without winning a Slam at that time, but the men's game is different. I believe the fact Rios is the only example highlights the strength of the sport and Andy is definitely playing in a really tough era with Nadal, Federer and Novak Djokovic all competing so hard.”

Despite praising Murray, Rusedski thinks he should focus on working on his second serve and forehand.

Rusedski said: “He has made significant improvements in all areas of his game this year and now it's a case of fine tuning those parts of his game that I have mentioned which are only minor weaknesses.

“Andy already has enough game' to win Wimbledon or the US Open and he is both mentally and physically ready to go two weeks in one of the majors and win the title.”

With a huge gulf between Murray and the rest of the men's game, Rusedski has been tasked by the Lawn Tennis Association with finding the next “big thing” in the British game.

Rusedski added: “Things are moving in the right way and we need to have a bit of patience but there are a number of good players at Under-14 level in Britain. I am very optimistic about the future of the game in this country.”