Murray has been going it alone, albeit with help from the rest of his team, since splitting with Ivan Lendl in March, a decision that came from the Czech, much to the Wimbledon champion's disappointment.
The setback may have hurt the Scot but he demonstrated that his game is close to its best when pushing Rafa Nadal all the way in the semi-finals in Rome last weekend.
The new coach - and there is no clear indication as to which path Murray will choose - is unlikely to be named until at least after his French Open campaign, which begins tomorrow.
Delighted to be here at all after missing last year's event through injury, Murray sounded confident yesterday as he discussed his form and fitness, eight months after undergoing back surgery.
The 26-year-old wants his next coach to be with him, ideally, for a number of years.
"[I will name the coach] whenever it's right, basically," said Murray, who will play Andrey Golubev of Kazakhstan in round one and could face Nadal in the quarter-finals.
"For me it's not about rushing into something. It's about getting it right, getting the right person. Until that's the case, I'll keep doing what I'm doing with, you know, the guys I'm working with. I have met a lot of good people that I respect and stuff and listen to their opinions on my travels, on the tennis tour. I'm not in a panic to get someone, but it's a lot closer than it was."
What the two-time grand slam winner did reveal, though, is that whoever comes in will be expected to deliver the same level of success that Lendl achieved.
"The target is the same, to win grand slams," he said. "That's what I want to do. I will pick the person I feel is best able to help me with that."
As the seventh seed, Murray faces a tough task to match his best-ever French Open run, a semi-final appearance two years ago.
But the Dunblane man's confidence was boosted by the way he played against Nadal in Rome, a match which also cast doubt on the Spaniard's chances of adding a record-extending ninth French Open title over the next fortnight.
Though he won the title in Madrid, the world No.1 has not quite dominated the European clay-court season as he has done in previous years, leading some to suggest Novak Djokovic is favourite to win his first French Open title.
Murray, for his part, could not care less what anyone else thinks. "Normally when the tournament starts, whether Rafa has been playing well or not, I would expect him to play great tennis here," he said, answering the question almost in spite of himself. "I would expect Novak to play great tennis here. Roger [Federer], I would also expect to play very well. That's what they have done. So there is nothing there to suggest that they are all of a sudden going to stop performing well in the slams and struggle. I would expect them to all have great tournaments."
Nadal marked his press conference here yesterday by saying he felt mentally strong after upping his game in Rome, even if he did lose to Djokovic in the final.
Djokovic says Nadal is the favourite, Federer says he is happy to be playing after having a second set of twins and Murray just wants to play.
"Rome was a good step forward," he said. "I need to build on that, take confidence from it, and I need to try to keep that consistency for the next four or five months if I can."