Murray beat Novak Djokovic to win his second Major title on Sunday afternoon, and McEnroe believes that the British number one will continue to improve his record in the four Major tournaments.
The American told BBC Sport: "I'd be surprised if he doesn't win at least six Majors.
"He's got a two, three, four-year period - a couple of years especially - where he's going to be tough to beat, really tough.
"He could win the US Open to have two Majors this year; no-one else would have that."
Murray's will head into this year's US Open as the defending champion.