Murray, seeded eighth, opens his campaign when he takes on world number 70 Robin Haase in the first round.
The Scot, who made his return from back surgery at the start of the year, arrives at Flushing Meadows on the back of three successive quarter-final defeats, and without a title or a win over a top-10 player since his 2013 Wimbledon victory.
His last Grand Slam outing saw him lose out in the last eight against Grigor Dimitrov at Wimbledon 2014 but according to Henman it would be foolish to rule out Murray's challenge as he goes in search of his second US Open title.
"I think he has got a good chance in the US; he had some good matches in Cincinnati and I think he looked very good," said Henman, who won Olympic doubles silver at Atlanta 1996.
"His game looks in good shape and physically he looks really good, which has been an important factor returning from back surgery at the end of last year.
"It hasn't been too straightforward for him but he's won the US Open before and the hard court is one of his best surfaces so I'm sure he can have a good run.
"He has won enough in the past; he has won so many Masters Series events, he's won two Grand Slams and he has won Olympic gold - and you don't forget how to win.
"He just needs to string it together and I feel like he's getting more and more match play under his belt so hopefully it can all click in New York.
"His ranking might be a bit further down but he's still one of the four or five favourites."
Despite Murray's early Wimbledon elimination this summer, Henman was adamant the current British number one should keep faith with new coach Amelie Mauresmo.
The former world number one was picked after a trial period to replace Ivan Lendl after the pair split in March following two years together and Henman believes another long term partnership was key.
"I was surprised when they made the initial announcement, I wasn't really sure who would take over after Lendl," he added.
"I think it's important now that they've got time for that relationship to grow. "It's difficult starting with a new player-coach relationship in tournament play, let alone when you're playing at home two weeks before defending the biggest title in the world.
"The remainder of this year is an important time to see how the relationship evolves. Hopefully it works out because I think the continuity is important for Andy.
"He doesn't want to be chopping and changing coaches. He wants a clear plan in place about the way he wants to play the game."
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- Grigor Dimitrov