Mamardashvili kept a clean sheet in Sunday's 0-0 draw with Rayo Vallecano.
The Georgia international is being linked with a big money move away this summer, though he insists his preference is to stay.
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Mamardashvili said afterwards: "My dream is that, but it doesn't depend on me, I don't know yet, we'll see what happens."
Marca says Valencia owner Peter Lim plans to sell the keeper this summer.