The Frenchman, who played under Moyes at Everton, thinks that the new man is "fighting against time".
He does believe Moyes can succeed, as he is driven by working hard and developing players.
"I have no doubt that Moyes will be a success at Manchester United," Saha told reporters. "But there is also no doubt that he is fighting against time.
"When you are in his position it comes down to how long it takes to put the team together, find the right tactics and get the best out of them. He is driven by an obsession to develop players.
"He is obsessed with working hard every day, working hard to improve the mentality of his players and every aspect of their game. He is a tough manager - including being tough on himself - and that is an asset for any club."
Saha scored 42 goals in his time at United, and 35 for Everton while Moyes was in charge.