A lengthening cast have been linked with the role, from John McEnroe to Jonas Bjorkman, Bob Brett to Larry Stefanki and, most recently, Martina Navratilova to Amelie Mauresmo, who watched his first match here.
After dispatching the Australian Marinko Matosevic for the loss of seven games - he won 6-3, 6-1, 6-3 - Murray tried to end the questions, for now. "Since stopping working with Ivan [Lendl, from whom he split in March], in the last five or six weeks, every week there has been a different person I am supposed to be working with," a rather irritated-sounding Murray said last night.
"I am not going to speak to anyone during a grand slam. I am concentrating on playing here for the next couple of weeks and then when I get on the grass I can start looking and get someone in place."
Murray did say that he had not spoken to Mauresmo, the former world No.1 who moved herself up the betting list when she sat through all four sets of his first-round win over Andrey Golubev of Kazakhstan. Navratilova, who has also been linked with the role, told BBC Radio 5 Live yesterday that she had not been contacted by Murray.
Yet the Scot, who next plays Germany's Philipp Kohlschreiber in the third round, said that he had not ruled out anyone, including Mauresmo. "When the time is right I will make an announcement," he said. "But nothing to say just yet. I like all of the people that have been mentioned. I have a good relationship with most of them. No bad names there."
Having taken four sets to get past Golubev, Murray was keen to avoid any more time on court than he required against Matosevic, an Australian whose "Mad Dog" reputation is better known than his tennis.
Though Murray said Matosevic deserved his nickname, it is a moniker that the 28-year-old dislikes, claiming his reputation for on-court histrionics and off-court pranking is undeserved. Yesterday, he did not argue with the umpire or break any rackets but he did produce a colourful range of language that the crowd, seated close to Court No.1 in Paris, will surely have heard.
Murray has been known to utter one or two swear words on court and in such an intimate atmosphere, a player's mood can be magnified.
"When you're out on the court, sometimes you say things," Murray said. "Obviously, when things are going well it's a lot easier to control your emotions. It something that over the last five, six years, I think, progressively has got better and something that I've worked on and tried to get better at and practise. It's something I can still improve on, aside from all the stuff that you can work on in your game. That's still something I'm working on today."
Right from the start, Murray looked to attack the Matosevic second serve and at times he was several feet inside the baseline when he made contact. An errant backhand gave the No.7 seed an early break but he had to save a break point to stay ahead at 3-1.
Matosevic was busy swearing to himself, mostly under his breath, as chances came and went, none more so than when Murray dug himself out of 0-40 to extend his lead to 5-3. "That's exactly what happens," the Australian said, to general confusion.
Murray then broke for a second time to wrap up the set and ripped through the second before an opening game in the third set that lasted almost 15 minutes. The Scot won it and then eased through the rest of the set to take his place in the third round. "I was just trying to make sure that my intensity was there every moment, especially at the beginning of the sets. I managed to get ahead early in all of them, and that helped."
Rafael Nadal believes that Dominic Thiem is a big name of the future but for now the Spaniard remains the one to beat, and he gave the young Austrian a lesson in clay-court tennis with a 6-2, 6-3, 6-3 victory. Unfortunately for Thiem, who possesses a huge game, Nadal was ready for him and despite going down a break in the third set he recovered quickly to advance to the third round. "It was a dangerous match and a dangerous opponent today," the eight-time Roland Garros champion said. "I played well, the way I would like to play."
David Ferrer, Gael Monfils and Fabio Fognini were among the other winners yesterday; today it is the turn of Novak Djokovic and Roger Federer to try to match them.