The 32-year-old, who suffered a long-term knee injury back in March, has been a free agent since the summer after his contract at Barcelona expired following a 12-year spell at Camp Nou.
The Spaniard, who was close to moving to Monaco before the deal fell through, was recently heavily linked with a free transfer to Liverpool, but manager Brendan Rodgers recently suggested that a deal was not going to happen.
Now, it has been confirmed by United that manager Louis van Gaal has reached out to Valdes to offer him the chance to continue his rehabilitation at the North-West club.
A statement on the club's official website said: "[Valdes] will have his recovery supervised by the United medical staff before training with the first team, as he bids to regain full fitness."
United have made no suggestion that Valdes will sign a contract with the former Premier League champions.