The three-time major champion is preparing for the defence of his Wimbledon title, while Jamie will be among the favourites in the doubles with partner Bruno Soares.
Murray and Soares, who also won in Stuttgart earlier this month, beat France's Julien Benneteau and Edouard Roger-Vasselin 6-2 6-3 to claim their sixth tour title together on Sunday.
"I'm pretty sure before they get to the end of their careers they're going to have a crack at Wimbledon doubles together", Judy said. I think we'd probably quite like to. Andy's always said he'd like to, but whether he follows through or not, I don't know!
"Obviously now it's too hard for him because singles is obviously a big priority, and physically it's so demanding".
"But on Monday (at Wimbledon) everyone starts from the same position... but we are one of the favorites for the tournament and we will do as well as we can".
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'For now, I'm happy with my partner.
Murray, who had been scheduled to face Frenchman Lucas Pouille, could still play in a further game at the Aspall Tennis Classic on Friday.
Jamie's victory - his first title at Queen's Club in 11 attempts - came on the same day that his mother, Judy, revealed that she believes her two sons will one day team up to try and win a Wimbledon doubles title.
The 30-year-old last played at Hurlingham in 2014 after he lost in the last 16 at Queen's.