Jamie signalled his eagerness to form an all-Murray duo one day at the All England Club but said he was happy with his current partner after they beat French pair Julien Benneteau and Edouard Roger-Vasselin in the final at Queen's.
Their 6-2 6-3 victory ensures at least one Murray triumphed on the grass this week after Andy's shock first-round exit to lucky loser Jordan Thompson in the singles on Tuesday.
"I'm not rushing to call Andy up and ask him when he wants to play," Jamie said with a smile.
"Yeah, I think one day we will probably try to play at Wimbledon. I think we'd probably quite like to.
"He's always said he'd like to, but whether he follows through or not, I don't know.
"It would be cool I think when we're kind of more towards the end of our careers to have a go at it.
"Obviously now it's too difficult for him because singles is obviously a big priority, and physically it's so demanding.
"I imagine when he starts to get a bit older and his level drops off a bit, we might have a go in the doubles one day. But yeah, for now, I'm happy with my partner."
Jamie won his first title at Queen's in 11 attempts and becomes the second British man to win the doubles at the venue in the Open era after Jeremy Bates achieved the same feat in 1990.
Murray and Soares have proven a strong partnership since joining forces at the start of 2016 and next month will look to add a Wimbledon title to the Australian and US Open crowns they won last year.
"Andy didn't play so well but we've been a bit spoilt with him over the years," Jamie said with a smile.
"What with him winning the singles five times it was nice that maybe I could take over for one year."
This is Murray and Soares' sixth ATP title together and in a twist of fate Murray lost his last doubles final at Queen's in 2014 when Soares was the other side of the net.
"Of course it's better this time," Soares said. "For me it was good both times but having the crowd on my side now it's a bit better."
Benneteau added: "You were too good today. At least one Murray won the tournament this week - it's a tradition here."
