Coach-less Murray earned praise for his new attacking style of play on the way to his first title of the year in Toronto earlier this month.
And Gilbert believes the Scot, who was beaten by Mardy Fish in the quarter-finals of the Cincinnati Masters last week, needs to carry on in the same vein at Flushing Meadows.
“I have never seen Andy Murray play more positive and aggressive tennis than in Toronto,” said Gilbert.
“By nature he likes to play defensive, but it’s so much more enjoyable and fun to play offensive and win offensive. That’s what he’s doing and what he needs to do to win majors.
“At 23 years old he is coming into his own and now it’s just a matter of getting to the finish line but he really believes he can do it.”
World No4 Murray is still waiting for his first Grand Slam title but will be among the favourites when the US Open begins next week.