The Spain international announced earlier in the season that he has no intention of penning a new contract at Camp Nou.
With his current deal set to expire in 2014, Barcelona may be forced to cash in on him once the transfer window re-opens rather than risk losing him for nothing.
A number of clubs are said to be interested in speaking with Valdes, with Anzhi among them.
The ambitious Russian outfit would be able to put an appealing financial package to the 31-year-old shot-stopper, placing them in pole position to secure his services, but they insist that no discussions have been held regarding an approach.
A statement released on the club's official website read: "In connection with numerous reports on the internet that Anzhi are holding talks with several players regarding possible transfers, including Victor Valdes, we announce that this information has no grounds.
"Anzhi will inform their fans and the media about all additions and signed contracts in due course."