Mrs Murray was photographed wearing a Freida maternity top at Centre Court at Wimbledon while she cheered on her husband and his doubles partner Serena Williams.
The couple have two children already but have not yet announced whether they are expecting a third. Andy and Kim Murray married four years ago at Dunblane Cathedral and are parents to two daughters - Sophia, three, and Edie, who is one.
One fan tweeted: "I’m convinced that the lovely Kim Murray is expecting her and Andy’s third child."
Another added: "Looks like Andy and Kim Murray are expecting another baby - Congrats to them."
Serena Williams and Andy Murray triumphed over opponents Fabrice Martin and Raquel Atawo in straight sets.
The Scotsman has approached the Murrays for a comment.