The Irishman has been the Reds' trusted second-choice goalkeeper behind Alisson since making his debut for the club in 2019.
Kelleher has mostly featured in cup competitions and has only 20 Premier League appearances to his name across six seasons.
Liverpool announced in the summer that Georgian Giorgi Mamardashvili will join from Valencia ahead of the 2025/26 campaign.
This means Kelleher could drop down the goalkeeping pecking order at Anfield, but first-team football could be offered elsewhere.
As reported by The Sun, Chelsea are tracking the 25-year-old ahead of a potential move next summer.
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It said that the Reds may be unwilling to sell a player of his quality, with a valuation of £35million, to a Premier League rival though.
However, Chelsea could help facilitate a departure should they meet the asking price.
Italian giants Juventus and Napoli are also understood to be keen, but it's claimed that Kelleher would prefer to stay in the Premier League if possible.
Robert Sanchez is Chelsea's current no.1 under Enzo Maresca, with Filip Jorgensen being their cup goalkeeper since his summer arrival.
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Marcus Bettinelli and Lucas Bergstrom are other options, with players including Djordje Petrovic and Kepa Arrizabalaga out on loan.
Despite such strong competition for places, Kelleher would be a top acquisition for the Blues should they agree a deal with Liverpool.
Alisson's recent absence with a hamstring injury has seen Kelleher start in Liverpool's last four Premier League matches.
He has also featured in their Champions League wins over RB Leipzig and Bayer Leverkusen, and the Carabao Cup win against West Ham.
However, even though Liverpool are unbeaten with Kelleher in goal this season, Alisson will be first choice again upon his return.
"He is and will be our first goalkeeper if he is fit. But first he needs to be fit," boss Arne Slot said via the Evening Standard.
"But Caoimhin has done outstanding, last season and this season again as well but the moment Alisson is fit, he will be our first goalkeeper."