Murray went under the knife for a second time five weeks ago in an attempt to finally overcome a problem that has dogged the Scot since the summer of 2017.
Speaking at Queen’s Club as he announced a long-term partnership with clothing firm Castore, the former World No.1 said: “I want to continue playing - I said that in Australia.
“The issue is, I don’t know whether it’s possible.”
Admitting he felt a renewed sense of positivity, Murray added: “I’m a lot happier now than I was, certainly in the last 12 months, because I have no pain in my hip now and I was in pain for a long time.
“The rehab is slow but it’s been going pretty well. I just need to wait and see how things progress. If it’s possible, I’d certainly love to compete again.”
Murray’s mum Judy stated yesterday that the 31-year-old would put his “heart and soul” into trying to return to professional tennis.
Speaking to Sky Sports she said: “He is doing pretty well. It’s not that long since he had the operation and time will tell.
“Nobody knows how he is going to recover in the longer term. He is in a good place mentally and we just keep our fingers crossed.
“But I tell you, if anybody can do it he can because he will put his heart and soul into it, like he does with everything.”
Murray said at an emotional press conference ahead of the Australian Open in January that he was planning to retire after this summer’s Wimbledon, but that the Melbourne tournament may be the last of his career.
However, a remarkable five-set defeat to Spaniard Roberto Bautista Agut gave the two-time Wimbledon winner renewed hope of making a comeback.
Although no player has undergone the same operation and returned to singles tennis, American Bob Bryan recently returned to playing doubles and won an ATP Tour title in Delray Beach in February along with brother Mike.
The Californian veteran has backed Murray to follow in his footsteps by making a comeback.