The Republic of Ireland goalkeeper is eager to become a senior No1.
Kelleher told the Athletic: "I have had a fantastic time in Liverpool. It's been a wild ride and I've loved it. I love the club, the fans and I have a good relationship with the players and the coaching staff."
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The 25-year-old feels he has to take the next step in his career, and he knows what that step entails.
"I don't know if it will be in Liverpool or somewhere else, but I feel that the next step is to become first choice," added Kelleher.