For the past five years, Kelleher has played second fiddle to the undroppable Alisson Becker at Anfield, often being restricted to EFL Cup and FA Cup appearances under Jurgen Klopp.
Since being promoted to the Liverpool first team in 2019 - four years after joining the Reds' academy from Irish outfit Ringmahon - Kelleher has played just 32 times for Liverpool, keeping 12 clean sheets in the process.
Only seven of those outings have come in the Premier League - including two matches against Fulham and Sheffield United earlier in the 2023-24 campaign - but he has played every minute of the Reds' EFL Cup run and started five of their Europa League group-stage games this term.
Klopp has always made it clear how highly he rates Kelleher, who has earned a reputation as one of the Premier League's leading number twos, but he has naturally been linked with a move to a club where he would be first-choice.
Back in the summer transfer window, Tottenham Hotspur and Brentford were reportedly running the rule over Kelleher, before both sides pursued other targets in the shape of Guglielmo Vicario and Mark Flekken.
Klopp also affirmed that it would take "extraordinary" money for Liverpool to consider selling Kelleher, who is under contract at Anfield for another two-and-a-half years, but according to The Mirror, Reds chiefs feel differently.
The report states that the club would be willing to part ways with Kelleher for around the £20m mark this year, and Celtic boss Brendan Rodgers has pursued a move for the Republic of Ireland international for some time.
Should Kelleher end his lengthy association with the Reds, Klopp supposedly wants Sunderland's Patterson as his new backup goalkeeper, having been impressed with the 23-year-old's displays for the Black Cats in 2023-24.
Patterson - who stands at 6ft 2in tall - came through the Sunderland academy system and spent a few months on loan with Notts County in the 2021-22 season before cementing himself as the Black Cats' number one.
The former England Under-21 international has eight clean sheets to show from 27 Championship outings in the 2023-24 campaign, taking his total for the club to 32 shut-outs in 105 appearances.
Patterson played every Championship game for Sunderland en route to the playoffs in the 2022-23 season, after which the Black Cats tied him down to a new long-term contract until the summer of 2028.
Prior to committing his future to the Black Cats, Patterson told the Sunderland Echo that he was content at the Stadium of Light, saying: "I'm obviously really happy here.
"This is my team, I have grown up supporting Sunderland. I'm happy here, content and looking forward to many more games. It's that extra bit special being able to play in front of the Sunderland fans and being able to be on the pitch rather than as a fan really."
Liverpool are not alone in their pursuit of Patterson, though, as Wolverhampton Wanderers and Leicester City are also said to be tracking his progress.