Nadal usurped Murray as world number two this week following his win at the Cincinnati Masters, meaning the Brit will be seeded third in New York.
While Nadal has won all 15 matches he has played on hard courts this year, Murray suffered a quarter-final exit in Cincinnati and before that lost in round three of the Rogers Cup in Montreal.
And Henman, speaking at Wimbledon where Murray memorably won his second Grand Slam earlier this summer, believes the 26-year-old will continue to battle with Nadal and world number one Novak Djokovic for Grand Slam titles in the coming years.
However, he is tipping Nadal to take Murray's US Open title from him when the Slam gets underway at Flushing Meadows next week.
"Andy has had a little bit of a slow start on the hard courts but he is there as defending champion and has got a great chance of adding another Slam to his CV," said Henman, who is the ambassador for HSBC Road to Wimbledon, the UK's largest junior grass tournament.
"Now he has got two Slams I definitely see him going on and adding more because he is that good - I think this is his time. Djokovic, Murray and Nadal I definitely see dominating the majors in years to come.
"But I would probably say Nadal is the favourite for the US Open right now. He is not number one in the world but he is the best player in the world this year - it is phenomenal he has only lost three matches.
"I would probably give him the edge, but Djokovic and Murray will not be far behind."
The HSBC Road to Wimbledon National 14 & Under Challenge is the UK's largest national junior grass court tournament and forms part of the HSBC's investment in the stars of the future.