The former Barcelona goalkeeper joined on a free transfer last season but has been frozen out after a disagreement with his manager, who accused him of refusing to play for the Under-21 side last term.
Valdes remains under contract at Old Trafford and tweeted a message on Wednesday stating that he will continue to work hard behind the scenes in order to earn a transfer in January.
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"Not to let down those who want to see me play again - that's my motivation," he wrote. "I fight to be free and enjoy my profession."
Valdes attached an image of him holding a piece of paper in his hand, which read: "What doesn't kill you makes you stronger."
Goal understands Valdes is likely to join Espanyol on a free transfer when the winter transfer window opens.