The Black Eagles have agreed personal terms with Valdes and will go ahead with the transfer after a final meeting with manager Şenol Güneş.
The Beşiktaş manager had raised concerns about Valdes last week but has now reportedly warmed to the idea of having the Spanish international as his first-choice keeper.
The Istanbul giants have been targeting a replacement for keeper Cenk Gönen who is expected to join Galatasaray.
Lions boss Hamza Hamzaoğlu told NTV Spor: “The transfer is almost a done deal, we have agreed terms with Cenk Gönen there are just a few details to go over.”
Valdes fell out with United boss Louis van Gaal over the summer and has not been selected for any games this season.
Van Gaal was speaking during a press-conference where United’s new transfer Bastian Schweinsteiger was unveiled when he stated:
“He [Valdes] is not selected because he don’t follow our philosophy. There is no place for that one player.
“Last year he refused to play with the second team.”
“When you are not willing to follow the principles of the philosophy there is only one way – out.”