Jamie revealed the pair had vowed to play together at the All England Club at least once before the end of their careers and hinted that this could be the year to do it.
Three-time Grand Slam champion Murray, 31, is currently recovering from a hip resurfacing operation which he had in January.
Footage emerged at the weekend of him hitting balls on one of the outside courts at Wimbledon, raising hopes of a return.
Lawn Tennis Association coach Matt James posted a clip on Twitter of the Scot playing with Estonia’s Annett Kontaveit, 15th in the women’s world rankings.
Doubles player Jamie said it would be “cool” to team up with his brother, who has been Wimbledon singles champion twice.
Asked about the possibility of the siblings appearing on court together, Jamie, 33, said: “Obviously people are talking about that and who knows?
“Maybe he will decide he wants to play doubles more regularly if singles is going to be too difficult after the surgery.
“That would be cool. We always talk like we want to play Wimbledon one time and maybe this year is our only chance. We will have to see but I hope that he gets back and he’s feeling like he can get out there and compete to the level that he’s used to.”
Murray, who has not played competitively since his first-round exit at the Australian Open in January, said last month he could possibly play at Wimbledon as he was now pain-free after the surgery.
Speaking on The Two Barrys Tennis Takeaway podcast, Jamie, who has won six Grand Slam doubles titles, also encouraged sports bodies and investors to get behind his mum Judy’s tennis centre at Park Of Keir near their hometown of Dunblane.
He said: “My mum has done so much for tennis in Britain and especially in Scotland. For me I want to see her Park Of Keir project get built. I know that she will make a huge success of it. I hope that she gets the investment to get it built whether that comes from the LTA or from private donors.
“I know how much she has put into it over the last five years to get it to this point but she needs financial support.
“For British tennis it would be a no-brainer to invest in that project knowing that she’s the person that’s going to be driving it and making it work.”
This year’s Wimbledon championships get under way on 1 July.