According to his mother Judy, the Scot will make an announcement about his match fitness soon.
"His goal was always to be ready for the grass-court season and, fingers crossed, that will happen," she told BBC Sport.
"I'm sure when he's got some news he will share that.
"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%."
Murray, who underwent hip surgery in January, was aiming to return to action in time for Wimbledon, but recent reports suggest that he could be forced to sit out the tournament.