Former world No 1 Murray underwent hip surgery earlier this year to try and rid his chronic pain.
The operation left him with months of rehabilitation and rose huge doubts over his career.
However, doubles legend Bryan has recently returned from having the same surgery and Federer hopes it will spur on his former rival.
“It’s great when they come back,” Federer said in his press conference after winning the Miami Open title.
“I’m sure also Bob is a big inspiration for Murray to come back.
“I hope that’s going to help Andy maybe finding a way back.”
Murray is hoping to return to full health ahead of Wimbledon.
But there are serious doubts over whether the three-time Grand Slam winner will ever be able to reach his former heights.
Meanwhile, Federer beat John Isner to win his 101st ATP title last night.
The Bryan brothers, Mike and Bob, won the Miami Open doubles title on Saturday, despite the latter being 40 years old.
Federer has explained why he and his American counterpart can still compete with the best players in the world.
“I don’t know. I guess definitely nowadays, with all the stretching and, I don’t know, silly elastic bands and stuff we do, maybe we can extend our playing days,” he added.
“Then you add diet to it and maybe more sleep and maybe not such a rock ‘n roll lifestyle that maybe guys were doing back in the ’70s and ’80s, all that stuff maybe takes away years of your life on tour.
“And also, prize money increase has helped maybe to keep some guys on tour, let’s be quite honest. Because if you know you can make as much money not traveling, at one point you’re like, I’m happy to stay home, and tennis was fun.
“But nowadays if you can stay on the tour and you can make a nice living, and actually traveling is easier now than ever before with the airlines we have and avoiding transits more and more, I think it’s much easier. I think all of those little things help.
“And then guys start doing ice baths and I don’t know what. I think all these things matter.
“What Bob is doing is definitely I think inspiring for a lot of the players, you know, even if it’s just doubles in the sense that it’s not as physical as the singles, as we know.”