The Spanish shot-stopper damaged his cruciate ligament in March, and has not featured in any competitive matches since.
The 32-year-old then announced he would not be renewing his contract at La Liga giants Barcelona, and he remains a free agent as he continues his rehabilitation work on his injured knee.
The gloveman has since joined up with the Red Devils in a bid to speed up his recovery and regain his fitness.
A stement released by Manchester United read: "Valdes will have his recovery supervised by the United medical staff before training with the first team, as he bids to regain full fitness."
The club did not reveal whether or not there was any intention to sign the player.
Valdes spent 12 years at Barcelona, featuring in 528 matches and winning six League titles, two Spanish Cups and three Champions League trophies.