Murray is fourth seed at Flushing Meadows in New York and the Swedish tennis legend, who won five consecutive Wimbledon singles titles, fancies his chances.
Murray beat Federer to win the Toronto Masters earlier this month, before reaching the quarter-finals in Cincinnati last week where he lost to Mardy Fish.
"For the men's singles I'm going to pick Andy Murray. He is definitely a player who can win Grand Slam tournaments. He's going to be up there fighting with Nadal and Federer from now on and one day he might be No 1 in the world," said 54-year-old Borg.
Moreover, the reigning champion Juan Martin del Potro is unable to defend his first Grand Slam title after failing to recover from a wrist injury.
"I think Andy will win his first Grand Slam - if he doesn't play Mardy Fish that is!" said another ex-Wimbledon champ Pat Cash.