The Uzbek is notable for being the only male player at the top level of the game to be coached solely by his mother.
Murray was coached by Judy when he was younger and she remains an important part of his support team.
Formerly the national coach for Scotland, Judy now works with Britain’s leading women and girls and is the Fed Cup captain.
Asked whether he could imagine being coached by his mother again, the Scot told reporters: “I wouldn’t rule it out.
“It’s not something I’ve thought about too much. But maybe when I start to come to the end of my career, it might be something that would be nice to do.
“Tactically she’s very good. She scouts a lot of matches and likes to watch videos of other players.
“My mum coached me and my brother until 11, 12 years old. Then I worked with Leon (Smith) for a long time.”