Kelleher is currently behind Alisson Becker in the Anfield pecking order and has seemingly seen his hopes of becoming number one quashed by the recent signing of Giorgi Mamardashvili.
The Georgian goalkeeper has been loaned back to Valencia, but he will be linked up with the Liverpool squad ahead of the 2025-26 campaign.
Speaking during the international period, Kelleher admitted that he had been left frustrated by his lack of regular game time and the club's decision to sign Mamardashvili.
The Republic of Ireland international revealed that he is keen to move on and find regular first-team action elsewhere.
Slot responds to Kelleher comments
In response to Kelleher's comments, Slot has insisted that he would have been more concerned if the 25-year-old was satisfied with being a backup goalkeeper.
Speaking ahead of Saturday's clash with Nottingham Forest, Slot told reporters: "I would be really worried if a player comes out saying, 'I don't care about playing first-team football.
"I like it so much on the bench that I want to stay there for the rest of my life'. That would be a bigger worry for me.
"So it's normal that they that they want to play, but it's also normal that a club like this, that tries to compete for trophies, has more than 11 players who can play.
"As long as they accept their situation, not accepting in a way I don't care that I'm not playing, but accepting it by helping the team whenever they have to, then it's a good place to be and Caoimhin has shown many times in the past few years and even in pre-season, that he's ready when he need him.
"So it's a good thing that he wants to play and who knows if he's going to play for us in the future. At this moment, I think it's quite clear that Alisson is the No 1, but last season he played many games.
Liverpool set to face one of Kelleher's admirers
Kelleher could have been lining up against Liverpool this weekend if Forest had been successful in their quest to sign him during the recent transfer window.
Nuno Espirito Santo's side reportedly failed with a late player-plus-cash offer, ensuring Kelleher remained a Liverpool player when the transfer window slammed shut.
As a result, Kelleher will be on the bench for Saturday's contest, while Matz Sels is set to line up between the posts for Forest.
Although a summer move failed to materialise, it seems likely that Kelleher will leave Anfield in search of regular playing time in 2025.
The goalkeeper, who has made 47 Liverpool appearances, is currently under contract with the Merseyside club until June 2026.