World number eight Murray, playing this week at the Madrid Masters, has been without a coach since he split from Ivan Lendl in March after a successful two-year spell during which he won two grand slam titles and gold at the 2012 Olympics.
"Every player would consider someone with his credentials," the 26-year-old Scot told the BBC on Sunday.
"I like listening to him commentate and he has a lot to offer as well. It's interesting but if anything comes from it, who knows?
"When you are very competitive as a player, you are likely to be the same as a coach and that's also a benefit.
"He was a great player and he's always kept an interest in the game, which is important. He has a great knowledge of the sport."
American McEnroe, 55, indicated this week he would be willing to help Murray, despite having a number of media commitments and a lack of professional coaching experience.
Murray, however, is in no rush to make an appointment.
"It depends how I do in the next couple of weeks," he said.
"If I do well, I'm not going to have that much time. If I don't do so well, I'll have a little bit more time to think about it and chat to people.
"I need to have the right person in place. I don't want to have the wrong person in place by the French Open. I'd rather wait a few weeks and get the right person three weeks after Wimbledon."
The French Open begins on May 25 and Wimbledon just over a month later.