The shot stopper has been invaluable for manager Jurgen Klopp in the absence of Alisson Becker.
Per The Mail, if Kelleher intimates that he wants to leave, then Liverpool will not stand in his way.
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The club do want a quick resolution to this saga in the summer, as they will want to secure a replacement.
Alisson is the undisputed number one and will be in that position next season as well.
Kelleher's future may also depend on who succeeds Jurgen Klopp as manager.