The Republic of Ireland international has played second fiddle to the Brazil international for the best part of four seasons and has been restricted to just 15 Premier League matches for the Anfield giants since joining in 2015.
Ten of those outings came in the 2023-24 campaign, when Kelleher earned plenty of plaudits for his performances in Alisson's absence through injury, despite only keeping two clean sheets.
However, the Brazilian quickly returned in between the sticks following his recovery, and the Reds bolstered their goalkeeping department in the summer window with the £29m signing of Giorgi Mamardashvili from Valencia, who will join the squad in 2025
At the same time, Liverpool priced Kelleher out of an exit from Merseyside, apparently rejecting a late player-plus-cash bid from Nottingham Forest as they held out for a fee of at least £25m and potentially up to £30m.
Kelleher: 'I've made it clear I want to be number one
Kelleher has also had to battle Gavin Bazunu for the number one spot in the Ireland team, but he benefitted from the Southampton man's Achilles injury to start in Saturday's 2-0 UEFA Nations League loss to England.
Ahead of Tuesday's second League B Group 2 contest with Greece, Kelleher opened up on a frustrating summer transfer window and confirmed that he wants to move elsewhere, but he admitted that the decision over his future is not entirely in his hands.
"I think I've made it clear in the last few years that I want to go and be a number one and play week in, week out. It's been reported that Liverpool rejected a few bids as well," Kelleher said.
"The club have made that decision to get another goalkeeper in as well which, obviously from the outside looking in, looks like they've made a decision to go in a different direction.
"So yeah, my ambitions have always been clear and has been clear the last few seasons that I want to go and be a number one. Sometimes from the outside looking in, it looks like maybe that's 100 per cent my decision but maybe at times it's not always in my hands as well."
Could Kelleher leave Liverpool in 2025?
It is hard not to feel sympathy for the 25-year-old, who has sometimes been labelled the best number two on the planet, but he has the unenviable task of playing backup to one of the best number ones on the planet.
Forest's bid in the summer apparently consisted of £7m plus Matt Turner, which Liverpool rejected outright after also turning down £15m from the Tricky Trees in January. Rebuffing those offers were understandable, but a £30m asking price was perhaps a bit steep; interested parties may not have baulked at a £20m valuation.
Regardless, the Liverpool board will have to relent on their price demands either in January or next summer, as Kelleher's contract only runs until 2026, and his recent admission suggests that he has no intention of extending.
Slight uncertainty surrounding the future of Alisson may complicate Kelleher's situation, as the Brazil international is allegedly looking likely to leave for Saudi Pro League next year, at which point Mamardashvili would replace him.
However, Liverpool have a handful of academy goalkeepers ready and waiting to inherit the number two position, so Kelleher's exit in 2025 is surely inevitable.