The Republic of Ireland international is second choice behind Alisson Becker at Anfield.
But he has gotten more game time this season as Alisson was suffering from a hamstring injury.
“I wonder with Kelleher longer term, I think he's established himself well enough now he won't want to hang around next season anyway,” the former Blackburn and Celtic striker said, per Nottinghamshire Live.
“He's certainly proved himself as probably one of the best backup keepers, if not the best backup keeper I think I've ever seen in the Premier League and he won't want to hang around at Liverpool next season, I suspect.”
“Yeah, he's done enough,” ex-West Ham goalkeeper turned pundit Rob Green added.
“I think (Giorgi) Mamardashvili, signing him for £25M or whatever it was kind of the final nail in the coffin for him.
“If this is his (Alisson’s) long goodbye before going off to Saudi or somewhere like that, then it seems a really bitter pill to swallow to say ‘Well, we've already made a decision and you've got to hang around until he comes along’ is adding insult to injury and it just goes to show how well he's done.
“But this is his window and I think that's too much for me. You sit there and go ‘I've proved myself at every opportunity and still this is how I get treated. Thanks but no, thanks.’”