The 55-year-old New Yorker, a seven-time grand slam singles winner, has so far proved resistant to the trend of former stars hooking up with current players on the tennis tour, a development - pioneered by Ivan Lendl working with Murray - which has Boris Becker coaching Novak Djokovic, Stefan Edberg in tow with Roger Federer, Goran Ivanisevic in tandem with Marin Cilic and Michael Chang in Kei Nishikori's corner.
McEnroe has numerous other demands on his time, most notably media duties with ESPN, CBS and the BBC, his own John McEnroe Tennis Academy in Manhattan, and competing on the seniors tour - it will bring him to the Brodies Champions of Tennis event in Edinburgh for the second successive year this June - but he admitted last night that the prospect of joining the influx was "tempting" and that he would be happy to pick up the phone and discuss the matter with the 27-year-old Wimbledon champion.
"It is nice to see some of these players closer to my generation, or some younger, still involved in the game," said McEnroe. "It is a nice shot in the arm for them as well as the sport, although my phone certainly hasn't been ringing off the hook, let's put it that way. I am pretty busy doing my own thing, but at the same time I suppose that if the right situation came along . . . when you get opportunities to coach great players it is certainly something that is tempting. So, of course I would answer the phone and think about it."
While the cachet of having one of the greatest players in the history of the sport in your corner would be quite something, in all likelihood Murray will opt for a full-time coach on the tour when he completes his recruitment process in the next week or so. The world No.8 has said he hopes to add a coach to his entourage before the French Open on May 25, with such as Bob Brett and Darren Cahill being linked with the post, and McEnroe sees no reason why the Scot should not be besieged by offers.
"I don't think you can just simply pick up and turn to another person that easily," said McEnroe. "That is probably part of the reason why he is not with someone right now. But I am sure at some stage he will find someone that he is willing to take that chance with and I am sure there are plenty of people who would love to do that. It is not as if it isn't a great job, to get the chance to work with someone as good as him. It is just a matter of him settling down and deciding where he wants to go."