The Black Eagles have agreed terms with Valdes a source close to the club told Turkish-football.com.
The Istanbul giants are however, concerned about the state of his fitness and want to run several tests before completing his transfer.
Beşiktaş are worried that he could arrive at the club injured and want to ensure he is ready for first-team football from the get go.
The Turkish Super league outfit are targeting a keeper after confirming that Cenk Gönen will be leaving the club.
Gönen is expected to join Galatasaray which will leave Beşiktaş lacking depth in the goalkeeping department.
The Eagles have had a busy summer bringing in several transfers including Quaresma, Mario Gomez and Andres Beck.
Beşiktaş will compete in the Europa League group stages this season and are manager by former Turkish national team manager Şenol Güneş.