Mary Pierce would be surprised if former Wimbledon champion Amelie Mauresmo became Andy Murray's new coach.
Murray revealed before the French Open that he had decided on the person he would like to succeed Ivan Lendl.
The name remains a closely guarded secret, and nothing is likely to be announced until after the tournament, but Murray was careful to be gender neutral in his answers.
Mauresmo, the current France Fed Cup captain, is a name that has been mentioned in association with the role but it was not until she was spotted watching Murray's first-round win over Andrey Golubev from close to his support camp that speculation really grew.
Mauresmo's countrywoman Pierce, a former French and Australian Open champion, told BBC Radio 5 Live: "I know there has been a top men's player who's had a women's coach before, but I'd be quite surprised if it was Amelie.
"But hey, anything is possible. I did notice that she was watching his match yesterday and I thought to myself, 'Why is Amelie watching this match?' We'll know soon won't we."
Mauresmo has coached a man before having worked with Frenchman Michael Llodra, while she was a key presence in Marion Bartoli's shock Wimbledon victory last summer.
The 34-year-old will have a good appreciation for the pressure on Murray's shoulders have carried the weight of French expectation for many years.
She never made it past the quarter-finals at the French Open but had a golden year in 2006 when she won both the Australian Open and Wimbledon.
Murray still has a considerable team around him at Roland Garros even without a head coach and he insisted after facing Golubev that he has been able to put the situation to one side, saying: "It's not something that's distracting me right now."
The 27-year-old has said in the past he would be open to having a woman coach, and has also mentioned the possibility of being coached again by his mother Judy later in his career.
Murray was not at his best against Kazakh Golubev but was content just to avoid an early exit.
The Wimbledon champion dropped a set on his first appearance at Roland Garros in two years but never looked in real danger of following the likes of Stan Wawrinka, Li Na and Grigor Dimitrov out of the tournament.
Golubev is a flashy player who, along with the cold and windy conditions, made Murray's life difficult before the Scot ground out a 6-1 6-4 3-6 6-3 victory on Court Suzanne Lenglen.
The 27-year-old, who missed the tournament last year with back problems, said: "It was tough conditions. It was obviously windy, especially at the beginning of the match, and very heavy conditions, cold and slow.
"He goes for his shots a lot. And there wasn't too much rhythm out there. It was a tricky match.
"I won the match. I did enough. In the third set I didn't serve particularly well. For the rest of the match I did okay. I did what I had to do, and I got myself into the tournament now.
"There have been quite a few upsets here the last few days and tricky conditions. So the most important thing is to get through.
"I've done a good job of that the last few years in the slams. I have not always played my best tennis at the beginning of the tournaments but I found ways to get through and give myself opportunities to do well in these events."
Murray next plays Australian Marinko Matosevic, who won his first match in the main draw of a grand slam at the 13th time of asking against Dustin Brown and celebrated by rolling around in the clay.