The 23-year-old has made exactly 100 appearances across all competitions for Valencia since joining the club in 2021, keeping 13 clean sheets in 37 league games last season.
Mamardashvili enhanced his reputation after starring for Georgia at Euro 2024 earlier this summer, remarkably making 29 saves in just four games which was at least 11 more than any other goalkeeper at the tournament.
The Tbilisi-born shot-stopper still has three years left on his contract with Valencia, but speculation over his long-term future with the La Liga outfit is rife amid interest from a number of European clubs.
It is understood that Valencia are prepared to sell Mamardashvili this summer if they received an offer between €35m (£30.1m) and €40m (£34.4m).
Liverpool leading race for Mamardashvili?
German giants Bayern Munich were credited with an interest in Mamardashvili earlier this summer, but the goalkeeper has stated that "it's currently not possible to move there" as Manuel Neuer remains their first-choice goalkeeper.
Recent reports have linked Liverpool with a move for the Georgian, with the Reds allegedly prepared to offer €30m (£26m) in a bid to lure him to Merseyside.
Both Bournemouth and Atletico Madrid are also said to hold an interest in Mamardashvili, with the latter understood to have identified the shot-stopper as a potential long-term replacement for Jan Oblak.
However, according to Spanish news outlet COPE, it is Liverpool who are the 'most likely' team to sign Mamardashvili this summer.
Mamardashvili interested in replacing Alisson as Liverpool's No.1
The report adds that Mamardashvili would be keen on joining Arne Slot's side if the opportunity was presented to him, but he would only be interested in a move to Anfield if he were to replace Alisson Becker as the club's number one goalkeeper.
It has previously been suggested that Liverpool may look to sign Mamardashvili and loan him back to Valencia where he would remain on a temporary basis until Alisson departs the club.
However, the Georgian has no interest in playing second fiddle to Alisson, whose future an Anfield is believed to be up in the air amid reported interest from clubs in Saudi Arabia.
Alisson is widely regarded as one of the best goalkeepers in world football and has spent the last six seasons at Liverpool, keeping 114 clean sheets in 263 appearances and winning a total of five trophies.
However, it has been reported that the 31-year-old Brazil international could have his head turned by a lucrative financial offer from the Middle East, as the goalkeeper approaches the latter stages of his career.