Mamardashvili signed for Reds for £30m this summer but will spend this season at Valencia and join the club next summer.
Kelleher has been a hero for Liverpool on multiple occasions throughout his career, namely in cup competitions in which he led the side to multiple trophies despite many underestimating him.
Now the Irish keeper is looking to leave the club as even though he has fought for his place in the side, Liverpool have signed a top keeper who is set to become a key starter.
Kelleher did not secure a move over the summer despite Liverpool rejecting an offer from Nottingham Forest and is now set for another season of cup football which is not ideal for the Ireland no.1.
“I made it clear in the last few years that I want to go somewhere and be a number one,” Kelleher said at a press conference on Monday, ahead of Ireland’s Nations League clash with Greece.
“The club has made that decision to get a goalkeeper (Mamardashvili) which makes it look like they’ve made a decision to go in another direction.
“Liverpool have rejected a few bids as well. It’s not always in my hands to fully make the decision. My ambition is clear. I’m good enough & I want to go and play week in, week out.”