The 23-year-old has spent the last three seasons with the La Liga outfit and has made exactly 100 appearances across all competitions, keeping 13 clean sheets in 37 league games last season.
Mamardashvili was also a standout performer for his country Georgia at Euro 2024 earlier this summer, remarkably making 29 saves in just four matches which was at least 11 more than any other goalkeeper at the tournament.
The Tbilisi-born shot-stopper still has three years remaining on his Valencia contract, but he has been strongly linked with a summer exit, with Los Che allegedly prepared to sell him for a fee between €35m (£29.6m) and €40m (£33.9m).
German giants Bayern Munich were credited with an interest in Mamardashvili earlier this summer, but the goalkeeper has seemingly ruled out a potential move to the Bundesliga club.
"Bayern still have the best goalkeeper in the world (Manuel Neuer)," Mamardashvili told Sky Deutchland. "It's currently not possible to move there. I would only go there if I'll play. If I don't play, then not".
Mamardashvili identified as Alisson successor by Liverpool
However, Liverpool have since emerged as a potential destination for Mamardashvili and according to Spanish news outlet Relevo, Arne Slot's side are prepared to offer €30m (£26m) in a bid to lure the Georgian to Merseyside.
The report adds that Mamardashvili - who is also said to be wanted by Bournemouth - would not immediately become a Liverpool player, though, and would instead be loaned straight back to Valencia where he would remain on a temporary basis until current first-choice shot-stopper Alisson Becker departs Anfield.
Speculation over the future of Alisson has been rife throughout this summer amid reported interest in his services from clubs in the Saudi Pro League.
Liverpool are said to be keen to keep hold of Alisson this summer, with the Reds currently having no intentions of cashing in on the 31-year-old.
However, it has previously been reported that the Brazilian's head could be turned by a lucrative financial offer from the Middle East, as the goalkeeper approaches the latter stages of his career.
Alisson, who has three years remaining on his contract at Anfield, is regarded as one of the best goalkeepers in world football at present and has spent the last six seasons at Liverpool, keeping 114 clean sheets in 263 appearances and winning a total of five trophies.