The 37-year-old British athlete underwent surgery over the weekend to address a back ailment, and he has since resumed training.
Murray, a former world champion who captured two of his three Grand Slam titles at Wimbledon, intends to step down later this year.
On Monday, the Championships get underway at the All England Club.
“I’m going to wait until the last minute to see if I’m going to be able to play, and I’ve earned that right to do that,” declared Murray, the 2013 men’s singles champion who broke Britain’s 77-year wait for a medal in the sport.
It’s not like there’s a 100% guarantee that I’ll be ready to play or a 0% possibility that I can. That’s the way it is.
In my opinion, the likelihood that I won’t be able to play singles anytime soon is higher.
The Scot had planned to compete at Wimbledon in both the singles and doubles, partnering with his brother Jamie, before his back issue flared up at Queen’s last week.