The two-time Wimbledon champion has been sidelined since last year’s tournament, and underwent hip surgery in January.
Murray’s mother Judy has insisted the 30-year-old can still be ready to hit form come Wimbledon’s July 2 start.
“His goal was always to be ready for the grass-court season and, fingers crossed, that will happen,” Judy Murray told the BBC.
“I’m sure when he’s got some news he will share that.”
Murray is unlikely to feature in a tournament in Loughborough later this month, while the Scot has publicly committed himself to Holland’s Rosmalen grass court tournament that starts on June 11.
“The strength and depth of men’s tennis is so great that I don’t think anybody would want to come back into that environment unless you are 100 per cent,” said Judy Murray.
Asked if she had any fears about his career being over, the former Fed Cup captain added: “I don’t think so; he’s still got a lot of things he wants to achieve in the game.”