However, the process may take a bit longer than he would like. "I would have someone in place before the French Open, but it's hard because there a lot of things that go into it with contracts and finances and stuff like that," he told the BBC. "What I have done over the last couple of weeks is I've got quite a few names down that I would be considering and taken some names off the list that wouldn't be suitable or would not be able to do it."
Murray has been without a coach since he and Ivan Lendl split just before Miami. He said the next person could be another well-known former champion or an experienced coach, as long as they met the requirements.
"It could be either," he said. "It's about how the two of you get on, how they see your game and how you are developing and the amount of time they can give you to do the job properly.
"And they also need to fit in with the team because I'm not going clear out all of the guys I work with and bring a coach in who wants to do things completely differently."
The defending Wimbledon champion was speaking at his hometown after receiving an honorary degree from the University of Stirling. With a month off from competition, Murray said it had also given him an opportunity to set about "speaking to a few people trying to find the right fit."
"I hadn't done that until 10 days ago," he said. "I wanted to concentrate on a few tournaments and, now I've had a bit of a break, I've had a chance to do that."