Walker, 33, is under contract at the Etihad until the end of next season, but negotiations over an extension to the England defender’s existing deal have yet to progress.
Sources have told ESPN that Walker is prepared to move to the Bundesliga to extend his career at the top level after becoming frustrated by the absence of a firm offer from City to discuss new terms.
The former Sheffield United right-back, who is also the subject of interest from Saudi Arabia, was dropped for the Champions League final win against Inter Milan in Istanbul last week with manager Pep Guardiola opting instead to use Manuel Akanji at full-back.
Guardiola had earlier cast doubt on Walker’s long-term prospects at City by saying in April that the player, a £45 million signing from Tottenham in 2017, was unable to adapt to a new tactical system which led to John Stones being preferred in a five-man defensive lineup.
But although Walker reclaimed his place in the side and was outstanding in the Champions League semifinal win against Real Madrid, and in particular in his direct battle with winger Vinicius Junior, sources have said that Guardiola is now ready to plan for the future by offloading Walker and replacing him in the squad.
There are also major doubts over the future of captain Ilkay Gündoğan, whose contract expires at the end of this month. On Friday, the midfielder was included on a list submitted to the Premier League of players who can leave on free transfers.
Gündoğan had been silent on his future after leading the club to the Premier League, FA Cup and Champions League trophies this season, with the Germany international linked with moves to Arsenal and Barcelona.
Information from Reuters was used in this report.