The Republic of Ireland international has played second fiddle to Alisson Becker ever since he was promoted to the first-team ranks, and Liverpool are understood to have blocked him from leaving for Nottingham Forest in the summer.
Kelleher made no bones about his frustration with his situation during the September international break, telling reporters that he has made it clear that he wants to leave and become a number one elsewhere.
However, the 25-year-old has benefitted from Alisson picking up more frequent injuries to shine in between the posts, and he has already played eight times in all tournaments this term, keeping four clean sheets.
Kelleher will be expected to drop back down to the dugout when Alisson returns from his latest hamstring problem, though, and Arne Slot's side will also welcome Giorgi Mamardashvili to the club from Valencia next year.
Chelsea rivalling two Italian clubs for Kelleher?
Whether Alisson sticks around for the 2025-26 season is another question entirely, but if the Brazilian does opt to spend one more year at Liverpool, Kelleher could be Slot's third choice next term.
As his contract also expires in 2026, a transfer in the summer transfer window appears inevitable, and The Sun claims that Chelsea could throw their hat into the ring for Kelleher's signature.
The report adds that Liverpool would naturally have reservations about letting Kelleher join another Premier League club, especially as Chelsea are currently mounting a Champions League charge in third place in the table.
However, the Reds may have no choice but to let him head for Stamford Bridge if Chelsea fork out a £35m fee, although the Blues must fend off the threat of Juventus and Napoli to land the Irishman.
Kelleher would supposedly prefer to remain in England if he is to call time on his Anfield career next year, though, giving Enzo Maresca's side an immediate head start over their Italian counterparts.
Which goalkeeper could Kelleher replace at Chelsea?
Stockpiling goalkeepers has been a theme for Chelsea over the past 12 months or so, but the Blues are supposedly still on the hunt for a new number one, as Robert Sanchez has not totally convinced in between the posts.
Summer signing Filip Jorgensen is also yet to be handed a chance to impress in the Premier League, while Kepa Arrizabalaga - still the most expensive goalkeeper ever - is on loan at Bournemouth.
The Spaniard will most likely secure a permanent move away from Stamford Bridge next summer when he enters the last 12 months of his deal, so Kelleher could very well take his place in the dressing room.
The 25-year-old may have a fight on his hands to usurp Sanchez and Jorgensen, though, and having been Liverpool's number two for most of his senior career, he will surely only consider moving to a new destination where he is guaranteed the number one jersey.
Kelleher has kept a total of 19 clean sheets in 55 games for Liverpool, who signed him for their academy from Irish outfit Ringmahon Rangers in 2015.