"I have never been past the quarter-finals of a Slam before so there is still a long way to go but it is up to me to continue to work hard and produce it on court - it is just a matter of putting it all together for two weeks."
The British number one's previous best ranking was eighth, which he reached in June 2007.
Murray's next tilt at a Grand Slam will come in the US Open at the end of August and he is aiming to continue his recent improvement when he goes to Flushing Meadows..
But his mother Judy has warned him that winning in New York would become more difficult if he has a successful Olympic Games.
The tennis event in Beijing begins on Sunday and lasts until 17 August, which will leave some players only eight days before the US Open starts.
And Judy Murray said: "The Olympics pops up at a difficult time in the tennis calendar, right after two Masters Series events and right before the last Grand Slam of the year.
"So it's really tough and it's a long way to travel as well, so I think it's going to be really difficult for tennis players
"I think anybody who does well at the Olympics is unlikely to do well at the US Open.
"But Andy will be going over there and really looking forward to being part of the British team and supporting the other athletes, and playing doubles with his brother.
"He'll be aiming to bring something home in some shape or form and if he plays well he has a good chance of doing that."
Murray's form at the start of the American hard court season, which saw him reach the semi-finals of the Toronto Masters before his triumph in Cincinnati, has meant he has swapped places with Andy Roddick of the US, who is now ninth in the rankings.
Switzerland's Roger Federer hangs on to the number one spot, but only until 18 August when he will be replaced by Spain's Rafael Nadal in top spot.
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