The 33-year-old former Barcelona keeper, who joined United last season when he was out of contract as possible cover for compatriot David De Gea, has made only two appearances.
United would not comment on Valdes's future on Thursday, but the player appeared to be saying goodbye when he posted a message on social networking site Instagram thanking the club's fans for their support, saying "I will never forget".
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(Reporting by Martyn Herman; Editing by Alison Williams)
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