Valdes joined Boro from Manchester United on a two-year deal at the start of the season, but is obviously keen to seek greener pastures after they made a swift return to the Championship.
The decision means the Teessiders will be desperately searching for reinforcements in goal during the off-season with second-choice keeper Brad Guzan set to join Atlanta United in the Major Soccer League.
Their only remaining gloveman at this stage is Dimi Konstantopoulos, who played just one game in the FA Cup against Accrington Stanley back in January.
While the squad is still a strong one for their upcoming campaign in England's second tier, the move could be an indication of a potential exodus of their top stars, which would put a big dent in their hopes of winning immediate promotion back into the topflight.