The 31-year-old recently revealed that he will not be signing a new contract at Camp Nou beyond his existing deal which expires in 2014.
The Catalan club have since made clear their intentions to sell the Spain international in the summer, and Red Devils boss Sir Alex Ferguson is keen to recruit.
With question marks remaining over the long-term future of current Old Trafford custodian David De Gea, Valdes has been identified by the 71-year-old Scot as a short-term solution to the problematic No.1 spot for Manchester United.
Earlier this week, it was reported by the Daily Express that Arsenal would also be interested in securing the services of the Spain international, with Wojciech Szczesny unable to convince Gunners boss Arsene Wenger that he is worthy of a first-team place between the sticks at the Emirates Stadium.
Valdes has had a decorated career at Barcelona, having been with them almost 23 years, and has lifted the Champions League and La Liga title on multiple occasions during his time in the first-team.
The Daily Mail reported at the weekend that it will take a bid of £10million for Barcelona to allow potential suitors to open negotiations with the want-away goalkeeper directly - a valuation that is affordable for both Premier League clubs.