After claiming that he would not rush the decision, Murray has now said that he wants someone in place before the second Grand Slam of the year next month.
"In an ideal world I would have someone in place before the French Open," Murray told Eurosport.
"That would be ideal for me, but things don't always work out perfectly.
"So, I need to think about it over the next 10 days or two weeks and really think about exactly what I want and what I need, and then go out and try and find the right person, but it's not always that simple."
The French Open begins on May 25.