The Bundesliga side currently have a man in the dugout, Gerardo Seoane, but the Swiss coach is on thin ice with his side second-bottom in the league.
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Leverkusen CEO Fernando Carro has said the club are not 'unprepared' when it comes to future planning, with an approach for Tuchel already made.
Sport1 have reported that Tuchel dismissed a move to the Champions League team, despite currently being on the lookout for work after being sacked by Chelsea in September.
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And now it's claimed by ESPN that Liverpool, Bayern Munich and Real Madrid great Alonso is in the frame.
Adored at Anfield for his Champions League heroics during a five-year spell between 2004 and 2009, Alonso then moved back to LaLiga to win another European Cup in Madrid.
The Spaniard, who retired from playing in 2017, began his career in management with his first ever club, Real Sociedad, managing their under 14s before moving up the the B-team.
Alonso received some big reviews for his work back home in San Sebastian, and was previously linked with the Borussia Monchengladbach vacancy when Marco Rose left in 2021.
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A three-time league winner in Germany, Alonso clearly made an impression, with Leverkusen now interested according to ESPN.
The 40-year-old former midfielder left La Real in June this year, and is currently without a job, meaning a transition to Leverkusen could be on the cards.