Murray was eliminated from the first round of the Australian Open on Monday, and said the match could be the last of his professional career, with the pain of his right hip having become unbearable.
Bryan, who has won 23 Grand Slam titles in men's and mixed doubles, and an Olympic gold medal with twin brother Mike, cut his 2018 season short in May and had hip surgery in August before returning to competitive tennis this year.
He said he had not advised Murray either way but hoped he would get the surgery to at least improve his quality of life.
"I'm just telling him, I feel great, quality of life is great, practices are going well," said 40-year-old Bryan.
"Maybe I'm not 100 percent yet, but I'm only five months. The doctors said this is more of like a seven or eight months until you feel perfect.
"Until I feel that, I can't give you the guarantee, but I think he's to the point where this is probably his last option.
"I would love to see him do it just for quality of life. You can sleep, walk, be with your kids, play. It's frustrating when you can't put on your shoes."
Bryan conceded that he was unsure how Murray's hip would hold up under the comparatively greater strain of singles.
"I never once told him this is the way to go because I do see that singles is a different monster," he said.
"Those guys are really sliding around, killing themselves for four hours. Who knows if this joint would hold up.
"It's not going to break, but who knows if you have that little explosiveness needed to be super quick on the singles court. If you're a step slow, it's very exposed out there on a singles court."
While limping and grimacing between points, a typically dogged Murray bowed out of Melbourne with a brave defeat in five sets to 22nd seeded Spaniard Roberto Bautista Agut.
An emotional Bryan struggled to compose himself in the media conference as he spoke of Murray's tearful media conference on Friday when he said he would likely retire this year.
"I stayed up till three in the morning watching all the tributes on social media," he said.
"It really hit a nerve with me. I mean, he's a special guy. No one has a heart like him. I think you guys saw the response he got from everyone."
"I personally think he can (come back from the surgery)," he added.
"But, you know, there's no evidence that it's possible in tennis. I mean, so much wear and tear. But I think he could do it." (Editing by Amlan Chakraborty)