Bayern's honorary president Uli Hoeness admitted their interest in Alonso but at the same time acknowledged the stiff competition they face from Liverpool and Real Madrid.
"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."