Having spent a few years as Alisson Becker's deputy at Anfield, Kelleher is now believed to be pushing for a move elsewhere this summer in search of regular game time.
The likes of Tottenham Hotspur, Brentford and Brighton & Hove Albion are all said to be interested in Kelleher, who could be sold if the Reds' £20m valuation is met this summer.
Liverpool are not expected to stand in the Ireland international's way of a summer switch, while third-choice shot-stopper Adrian is also out of contract at the end of the season.
Jurgen Klopp's side are supposedly already getting to work on scoping out replacements for Kelleher, and according to Bild, Zieler has emerged as a top candidate.
The 34-year-old is only under contract with German second-tier side Hannover until the summer of 2024, having seen an extension option in his current deal triggered in March.
Zieler was said to have been left unhappy with Hannover only exercising a short-term extension, handing Liverpool an early boost in their efforts to bring him back to England.
The German caught the eye of then-Manchester United boss Sir Alex Ferguson in 2005 as a teenager, and the Red Devils swooped to bring him to Old Trafford from Koln.
However, Zieler did not make a single senior appearance for the Red Devils and was shipped back to Germany with Hannover in 2010, although he was lured back to England by Leicester City in 2016.
The goalkeeper's stint at the King Power was not a memorable one, though, as he kept just one clean sheet in 13 appearances - nine of which came in the Premier League - before leaving for Stuttgart after just one season.
A former six-cap Germany international, Zieler was part of Die Mannschaft's squads at Euro 2012 and their triumphant 2014 World Cup campaign, although he did not play a minute at either tournament.
Zieler has eight clean sheets under his belt from 32 2. Bundesliga appearances in the current campaign, as Hannover sit eighth in the rankings with just two games left to play.
The Reds have apparently been alerted to Zieler's availability by Jorg Schmadtke, a former Hannover sporting director who is the favourite to take on the job at Anfield this summer.
Liverpool lost long-serving sporting director Michael Edwards at the end of the 2021-22 season, but only a few months later, the Reds were rocked by the news that his replacement - Julian Ward - would also be stepping down this year.
Klopp's side sit fifth in the Premier League table and can close the gap to fourth-placed Manchester United to just one point by beating Leicester City on Monday night.