Kelleher was named the best reserve keeper by former Reds manager Jurgen Klopp last season.
But Kelleher told talkSPORT: "It's not a title I want - I want to be playing week in, week out. At the moment the situation for me is I'll get these opportunities and I need to do well when I get these opportunities and play well, so that is my main focus obviously. Just when I do get that chance, play well."
"It is important I play week in, week out now and get that No.1 position. I have to show everyone I am capable and good enough to play week in, week out.
"I feel I have the quality to play well when needed, even if that means I'm not playing a game in a few weeks I can come in and still show my quality, so that's the most important part - to be ready when called upon."