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Instead, though, he opted to stay with Bayer Leverkusen and lead them into a Champions League campaign - one which ended in the round of 16 at the hands of Bayern Munich.
During the international break, though, there has been speculation in Spain that he's now ready to jump ship for the Bernabeu.
Madrid are reluctant to make their own decision on the future of Carlo Ancelotti until the summer, and there are plenty of variables there too.
Ancelotti's first Real Madrid spell came to an end in 2015, after a second-place finish in La Liga - albeit one where they scored an astonishing 118 goals - and a run to the semi-finals of the Champions League(
Alonso won the Champions League with Real Madrid and Liverpool, but opted against taking over at Anfield.
He opted to continue his development with Real Sociedad's B team rather than jumping into a top-flight job - with Borussia Monchengladbach the potential suitors at the time - and recognised he would be able to bide his time for another year or more at the BayArena.
There is still plenty of credit in the bank from the 2023-24 campaign, a season where Atalanta were the only team to beat Leverkusen in league, cup or European competition
Alonso won a league and cup double with Leverkusen last season
He has also overseen a Champions League campaign including wins over both Milan sides, an impressive achievement even if there will be some disappointment with how things ended in the knockout stages.
He is currently working with a relatively settled squad, free of the ego management that comes with managing a club of Real Madrid's size and stature