Having come so far in his rehabilitation from a tendonitis problem that forced him to undergo two operations in America in the last year, Sir Alex will not rush the final few steps in the 28-year-old's recovery.
"It's difficult to say [when he'll be back]," he said. "I have not got an answer to that one.
"He is doing plenty of work with the physios and he is doing a lot of football work. But I think it comes down to a confidence thing and knowing that he is ready to come back with our players. Hopefully that is sooner rather than later."
Hargreaves hit the training track yesterday morning with United teammates.