The experienced Serbia defender has slipped down the pecking order at the German giants and made just 11 appearances last season due to injury, but would be an impressive acquisition for a club in Boro's position.
Subotić to leave Dortmund with clubs interested
Subotić has already confirmed his intention to leave the Bundesliga side over the summer, and Dortmund announced on Thursday morning that he had been given permission to leave training to discuss terms with a potential suitor.
According to the Echo, Subotić has been shown around Middlesbrough's facilities, but with a number of clubs reported to be interested in his services, any deal could be some way off yet.
However, it is possible that the signing of Valdés - who was said to be impressed by manager Aitor Karanka's vision for the club - could help to persuade the 27-year-old defender that Boro are the club for him.
He has amassed almost 200 league appearances for Dortmund since joining from Mainz in 2008, winning two Bundesliga titles and one German Cup during his time at the club.
He also has two German Super Cups to his name, and played the full 90 minutes as Dortmund were beaten by Bayern Munich in the Champions League final at Wembley in 2013.
Subotić has work to do to win first-team spot
Despite this pedigree, it is unlikely that Subotić would be the immediate first-choice option for Karanka in the heart of defence, with the current axis of Daniel Ayala and Ben Gibson boasting a stunning record at the back together.
Middlesbrough had the best defensive record in England last season, and will be hoping to use their back four as the bedrock of a successful season in the top flight.