The 33-year-old appeared to be on the verge of joining the German champions last summer, before he was persuaded to stay by Man City boss Pep Guardiola.
After turning down a move to Germany, Walker subsequently put pen to paper on a new contract to keep him at the Etihad Stadium until June 2026.
Walker has continued to be a regular fixture in the Man City side this season, having made 41 appearances across all competitions.
The full-back recently provided two assists to help his team cruise to a 4-0 victory in Thursday's Premier League away meeting with Brighton & Hove Albion.
Although Walker is enjoying regular game time, he could still be presented with the chance to leave the Etihad Stadium this summer.
According to the Daily Star, Bayern are showing an interest in Walker and could revive their pursuit in the summer transfer window.
The German giants are seemingly keen to reunite Walker with his former Tottenham Hotspur teammate Harry Kane, who has racked up 35 goals since joining the Bavarians last summer.
Walker and Man City are both aware of Bayern's interest, but it remains to be seen whether the player has a desire to cut ties with the Citizens this summer.
Do Bayern need another right-back?
On the face of it, Bayern currently have a number of right-back options, including Joshua Kimmich, Sasha Boey and Noussair Mazraoui.
Josip Stanisic could also strengthen the right side of Bayern's defence when he returns from his loan spell with Bayer Leverkusen.
However, Sacha Boey has struggled with injury since arriving from Galatasaray in January, while Mazraoui has been linked with a move away from the Allianz Arena.
There is also a possibility that Kimmich could move back into midfield when a new manager replaces Thomas Tuchel at the end of the season.