The 23-year-old has made five appearances for the club's first-team this season.
However, Given believes that the Kelleher should be playing regular senior football at this stage of his career.
With that being the case, the 45-year-old has implied that the Irishman should seek a loan move away from Anfield.
As quoted by LFC Transfer Room's Twitter account, Given told Premier Sports TV the following: “He’s in a bit of a predicament, is Kelleher. He’s not a kid anymore. 23 is an age where I think he should be playing regular first-team football."
“Does Kelleher sit there and be happy as a number two? They’ve got Adrian who can sit on the bench and back [Alisson] up.
“For me, it’s so important to play games. He has been training there for a few years and signed a new five-year contract last summer, so he is part of the club’s long-term future.
"Even from a Liverpool point of view, they need to get him out playing, get him that experience, then bring him back and get him challenging Alisson.”
Anfield Watch Verdict
Given is spot on. The reality is, Alisson's career is far from over. The Brazil international is only 29 years of age.
Unless Alisson's performance levels drop dramatically, he will be a Liverpool player for many more years. As Given has pointed out, the shot-stopper's contract does not expire until the summer of 2027.
Therefore, we would like to see Kelleher go out on loan in the near future. There is only so much you can learn from playing the odd game here and there.
But, only time will tell where Kelleher's long-term future lies.