The Georgia international has impressed in his first season at the Mestalla Stadium, keeping nine clean sheets in his 21 appearances for the club.
Despite joining Valencia last summer from Dinamo Tbilisi, Mamardashvili could be heading through the exit door in the coming months, with the Copa del Rey finalists looking to raise up to €70m (£59.74m) in player sales this summer.
According to Marca, Tottenham Hotspur have shown an interest in the 21-year-old.
Although Hugo Lloris is regarded as the current number one, Tottenham are already thinking of a future replacement for the French goalkeeper.
The report suggests that a deal for Mamardashvili is plausible, with Tottenham and Valencia enjoying a good relationship following the loan spell of Bryan Gil, who spent the second half of the 2021-22 campaign at Mestalla.
Mamardashvili, who helped his side reach the Copa del Rey final, has two years left to run on his current deal with Valencia.