"Obviously when someone like that shows an interest, you have to take that into consideration because he is a great tennis player," Murray told the BBC. "He loves the game, is very passionate about it and was extremely competitive as well.
"I have always got along well with him."
McEnroe had told the Scotland Daily Record that, "if Murray picked up the phone and asked me to coach him, of course I would think about it."
"But my phone hasn't been ringing off the hook," McEnroe added. "I'm quite busy doing my own thing, but if the right situation came along and I got an opportunity to coach a great player it would certainly be something to think about."
However, the seven-time Grand Slam champion has a full commentary schedule at majors and would probably not be able to make the kind of commitment Murray has said he wants.
Murray and Ivan Lendl ended their coaching relationship before Miami, having won two Grand Slam titles together. Murray repeated that he has begun searching for a new coach, but said it would depend on his tournament schedule and that he did not want to go into details. British newspapers have said former players Larry Stefanki and Jonas Bjorkman are also among the candidates in contention.
"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," Murray said, adding in a pre-tournament interview that, "I don't want to go into any names because that would cause me [to get] questions over the next week or so, but it's something I did start to think about a lot the last couple of weeks."
Though he would like to hire a new coach by the French Open, Murray emphasized that he wanted to make the right move.
"I don't want to have the wrong person in place by the French Open," he said. "I'd rather wait a few weeks and get the right person three weeks after Wimbledon."