The 22-year-old has been sidelined since October with an ankle problem picked up in his side's 1-0 win against Everton.
The England international could now be named in the squad for United's Premier League match against Liverpool on Saturday, February 11.
"I am hopeful in ten days' time he will be playing football on the training side of it anyway," said manager Sir Alex Ferguson. "That is the plan unless there is any recurrence of the injury. Then we can kick on."
Cleverley has made five league appearances for the Red Devils this season.