The report claims that Beşiktaş want to run medical tests before completing the move.
The Istanbul giants have agreed terms with Valdes sources close to the club told Turkish-football.com.
Beşiktaş board member Erdal Torunoğulları is currently in England holding final talks with United.
The Spanish international keeper is expected to arrive in Istanbul within the next couple of days.
Valdes is expected to leave the Premier League giants after falling out of favour with head coach Louis van Gaal.
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.”