The 31-year-old underwent hip resurfacing surgery at the end of January in a final throw of the dice to try to overcome the problem that first became a serious issue in 2017.
"I want to continue playing, I said that in Australia," Murray said at a sponsorship event at London's Queen's Club.
"The issue is I don't know whether it's possible."
"I'm a lot happier now than I was, certainly the last 12 months, because I have no pain in my hip now and I was in pain for a long time," he added.
"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, who has won three Grand Slams, announced at an emotional press conference ahead of the Australian Open in January that he planned to retire after Wimbledon but was more hopeful following a remarkable five-set defeat by Roberto Bautista Agut in the first round.
No player has come back from the same operation to play singles but American Bob Bryan recently returned in doubles and won an ATP Tour title in Delray Beach last month with his brother Mike.
Bryan said in Australia that he no longer felt any pain and backed Murray to follow him by making a comeback.