Bayern Munich honorary president Uli Hoeness says the club are competing with Liverpool to appoint Xabi Alonso as manager.
Spaniard Alonso, a former player of both clubs, is on the brink of guiding Bayer Leverkusen to their first German Bundesliga title.
Bayern and Liverpool are both looking to appoint new managers this summer.
"Clubs like Liverpool, Real Madrid, Leverkusen and FC Bayern are working on it," Hoeness told Ran Sport.
"He's proven that he can be a coach for the big time. There are hardly any coaches who come into question who are currently free, who don't have a job or who are on sabbatical.
"It's not so easy to tell them that FC Bayern is the measure of all things."
Thomas Tuchel will leave Bayern Munich at the end of the season, while Jurgen Klopp announced his decision to step down at Liverpool in January. The Reds are second in the Premier League, level on points with leaders Arsenal.
Carlo Ancelotti, the Real Madrid manager, extended his deal with the club until 2026 in December. Alonso spent five years as a player at Real in between his stints at Liverpool and Bayern.
Alonso's deal at Leverkusen runs until 2026.