Murray was outclassed by Federer at Flushing Meadows in his first-ever grand slam final, going down 6-2 7-5 6-2.

But Henman told BBC Sport: "I really think he can be number one in the world - he is only 21 - and from Wimbledon earlier in the year it is amazing how much he has improved."

The former British number one added: "Andy has had many big breakthroughs and I think it is phenomenal how quickly his game is improving - he's up to four in the world now, so it's on to bigger and better things.

"There are so many areas he can improve on. His backhand is as good as there is in the game and he can be a bit more aggressive on his forehand.

"People were saying he got destroyed by Nadal at Wimbledon, but he played the match of his career to beat him in the US Open semis and it won't be long before he's even higher.

"I wouldn't have thought he'd waste any time worrying what other people think. Fortunately Andy is more focused on his own game and where he needs to improve."