Two-time champion and former world number one Murray underwent surgery to remove a cyst from his spine last week.
"The operation on the back wasn't insignificant," said 37-year-old Murray who will train again on Monday before deciding if he is fit enough to play his scheduled first round match on Tuesday.
"I don't have 100% feeling and sensation in my leg yet but it's getting better every day."
He added: "I want to give it every single chance that I can to get there. I'm going to play another set again tomorrow. I'm doing some physical testing in the morning to see sort of how far off I am. Then I will probably make a decision tomorrow evening."
Murray explained that the cyst compressed nerves and caused him to lose most of the control in his right leg.
"It's kind of like if you sleep on your arm funny, you wake up and you've got a dead arm," he said.
Murray is due to face Czech world number 38 Tomas Machac on Tuesday.
If he can't make that date, he still hopes to play doubles with brother Jamie before bringing the curtain down on his Wimbledon career which began 19 years ago.
"Obviously with doubles, although you're covering less distance and less court, you still need to be able to move pretty explosively," said Murray.
"I'm hoping that with each day that passes the likelihood of me being able to play will increase. It's impossible for me to say because I also want to go out there and be able to play to a level that I'm happy with."
Murray claimed his first Wimbledon title in 2013, ending Britain's 77-year wait for a men's champion, with a straight sets victory over career-long rival Novak Djokovic.
That was a triumph that did not lack a bump or two as Murray needed to come back from two sets down to defeat Fernando Verdasco in the quarter-finals.
'One more time'
Murray added a second Wimbledon title for good measure in 2016 with a straight sets triumph against Milos Raonic.
It was his third Grand Slam title, having picked up his first major at the US Open in 2012, just weeks after having lost to Roger Federer in his maiden Wimbledon final.
However, since his 2016 All England Club triumph, Murray has not passed the quarter-finals.
He missed the 2018 tournament with injury while 12 months later sat out the singles after undergoing hip surgery.
That year, he played men's doubles as well as mixed with Serena Williams.
Injury has been a constant problem for Murray in the twilight of his career.
He has played with a metal hip since 2019 while this season saw him damage ankle ligaments in Miami when he went down to defeat to Machac.
Murray made his Wimbledon debut in 2005, reaching the third round where he took a two sets lead before losing in five to 2002 runner-up David Nalbandian.
"Everyone has their idea of how they want to finish their career, how they would want it to go," he said.
"I probably would have seen that happening probably at Wimbledon. Obviously I have the Olympics coming up. But, yeah, I would love the opportunity to play here one more time."
