Reigning Wimbledon champion Murray parted company with Lendl in March and has so far been unable to find a suitable coach to work with.
26-year-old Murray expressed his desire to hire a new coach ahead of this year’s French Open. It appears that another legend from the Lendl era in the form of McEnroe could be the man to take on the role after the American expressed an interest in working with the current world number eight.
Speaking to the BBC, Murray said: “Every player would consider someone with his credentials.
"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?"
McEnroe, who was renowned for his fiery temperament on court, pursued a career in television following his retirement from the sport, but at the age of 55, could now take up coaching.
“When you are very competitive as a player, you are likely to be the same as a coach and that's also a benefit," added Murray.
"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."
This year’s Roland Garros tournament begins on May 25, which leaves Murray just three weeks to make an appointment, though he has stated that he may wait until after Wimbledon.
"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."
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