Two-time Wimbledon champion Andy underwent a second hip operation in January following the Australian Open and the 32-year-old is yet to set a date for a potential return.
This year’s Wimbledon gets under way on July 1.
Doubles star Jamie, having taken part in an event on Sunday testing the new Court One roof at Wimbledon, was asked if it was likely his brother would be playing on the court in the future.
And he said: “I hope so. I’m pretty sure he wants to be able to do that again at some point.
“He’s doing his rehab, I think he’s kind of on track with his recovery for where he is in terms of the timing of it right now.
“And I think his goal is just rehab, get his hip as strong as possible so that when he does get the chance to get back out on court and train properly, he’s best positioned to really find out what is going to be possible for him.
“He’s hitting a few tennis balls. He’s not like tanking it around the court or anything like that movement-wise, but as I said that is what he is building up to and I don’t know exactly when that will happen.
“He’s doing fine, pain-free and a lot happier obviously. So we’ll have to just wait and see. It’s just difficult to know what is going to be possible for him.”
Jamie has been playing golf with Andy, and added: “That’s his competition just now.
“He’s been starved of that for a while, so he’s been getting right into that, which is cool. Not so good for me because he is playing better than me just now!”
Jamie was also asked if he would ever play doubles with Andy, and said: “It’s something we do want to do at some point, but I guess it just depends on certain situations in both our careers. But I don’t think this year (it) will happen.”
Former Wimbledon champions Martina Navratilova and Pat Cash both expressed confidence Andy would be back playing at SW19 at some point.
Nine-time winner Navratilova said: “I don’t think it’s going to happen this year, I don’t think he’ll be quite ready.
“I just hope he takes his time so he can play pain-free, and I would not be surprised if he does really well here next year.”
Cash, champion in 1987, said: “I have no doubts Andy will get to play back here.
“I think he’s feeling very confident he’ll come back. I don’t know when it’ll be, and I’m not sure if Wimbledon is a little too early to expect that, but I think we’ll see him back here playing.”
Along with Navratilova and Cash, the former champions taking part in the ‘Number One Court Celebration’ event were Venus Williams, John McEnroe, Kim Clijsters, Lleyton Hewitt and Goran Ivanisevic.
As well as exhibition matches, the event featured music from Paloma Faith, Joseph Calleja and the BBC Concert Orchestra.
Navratilova said of the roof: “Fantastic. The court itself is playing great. I played yesterday when the roof was open and today when they closed it. It’s a little more humid, a little heavier conditions, but the atmosphere is just phenomenal.
“You almost don’t care whether you play on Centre or Court One now.”