ANDY Murray is giving himself enough chances to win a Grand Slam and is capable of winning many, according to his former doubles partner.

Derbyshire tennis coach Tom Rushby is also convinced the Scot, who is competing in the US Open this week, will become world number one someday.

Murray last night booked his place in the third round of the major at Flushing Meadows, New York, after beating Jamaican opponent Dustin Brown in straight sets last night.

Murray celebrated a 7-5, 6-3, 6-0 victory.

It is the 20th time the world number four has contested a Grand Slam tournament, as he bids to win his first major.

Rushby, who played in the semi-finals of Junior Wimbledon with Murray in 2003, said the British number one went into the tournament in good shape.

The 24-year-old said: "You feel in every Grand Slam that Murray's got a good chance but he has just won Toronto and he looked good in his US Open first-round match too.

"But, more importantly, it is the first time he has beaten both (Rafael) Nadal and (Roger) Federer in a tournament, beating them both in Toronto.

"He's almost the best of the rest of the other players and it's just the top two he can't quite get past.

"So, to beat them back-to-back like that must be a massive confidence boost for him and something he can take into the US Open and other tournaments.

"And, if he brings his A-game to the Open, he really does have every chance of winning the tournament."

This year, Murray has had promising results during the previous three Grand Slam tournaments.

January saw him reach his second major final at the Australian Open, before he lost in straight sets to 16-times Grand Slam title-winner Federer.

At the French Open, in May, he was defeated in the fourth round of the clay-court tournament by the Czech Republic's Tomas Berdych.

He followed this up by reaching the semi-finals of Wimbledon, where he lost to world number one Nadal, of Spain.

Rushby, who works as an academy coach for Midlands Tennis in Loughborough, said it was good to see the amount of chances Murray was giving himself to win a Slam.

He said: "That was one of (Tim) Henman's biggest problems.

"He was an unbelievable players but he often lost in the quarter-finals of majors and didn't give himself enough chances to win them.

"But Murray is doing that. He is putting himself in a position where the law of averages suggests he has to win one at some point."

He added: "Let's not forget that he is still only 23 and pretty young, with plenty of time ahead of him.

"Nadal is only a year older but he does sometimes have knee problems because of the workload he puts on his joints, so you wonder how long he can keep that up.

"And Federer is now 29, so he's not got years and years ahead of him. If Murray can keep up his form, he can eventually become world number one. He is capable of doing it.

"The other thing to remember is that Murray can still improve his game, if only slightly, while the other two are pretty much at their full potential.

"If Murray can up his first serve percentage and perhaps improve his forehand, he has every chance to win."

Rushby, who first played alongside the Scot at the age of 14, said if one of either Federer, Nadal or Murray were in the US Open final, they would probably win it.

He said: "You do get the odd player who bursts through to the final, like (Novak) Djokovic, (Robin) Söderling or Berdych but it is usually those three at the end.

"Obviously, it would be nice if Murray did reach the final and found someone else there but I can't see it happening.

"The draw was not in his favour when he got Nadal in his half and I don't think the fact that Nadal hasn't won this tournament will have any effect on him, because he's won the other three.

"It will be a big ask to take out Nadal in the semi-finals and then Federer in the final, if they all get there, but he does favour the hard court.

"I thought he had a good chance at Wimbledon but he is a good counter-attacker here, so he just needs to get the job done."