Thomas Tuchel will leave Bayern at the end of the 2023-24 campaign, with the biggest managerial job in German football therefore set to become available.
Liverpool, meanwhile, will lose Jurgen Klopp this summer, with the Reds facing the difficult task of replacing the inspirational figure.
Alonso's work at Leverkusen has allegedly made him the leading managerial target for both Bayern and Liverpool this summer, and Hoeness has claimed that the pair are «working on» a deal for the Spaniard.
Real Madrid have also been mentioned as candidates, although the Spanish giants have recently extended the contract of their current head coach Carlo Ancelotti until the summer of 2026.
«He's [Alonso's] proven that he can be a coach for the big time,» Hoeness told Ran Sport. «Clubs like Liverpool, Real Madrid, Leverkusen and FC Bayern are working on it.
»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."
Bayern would allegedly have to pay between €15m (£12.8m) to €25m (£21.3m) to bring Alonso to Allianz Arena this summer, and various reports in Germany have claimed that the former midfielder would prefer to move to the Munich giants over Liverpool at this stage of his career.
Alonso, 42, started his coaching career with Real Sociedad B, managing the La Liga club's second team between June 2019 and May 2022 before taking charge of Leverkusen in October 2022.
The Spaniard has won 50, drawn 15 and lost
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