The in-demand coach opted to stay at Leverkusen this summer, despite strong links to former club Liverpool, who were searching for a new manager following the exit of Jurgen Klopp.
Alonso also turned down a move to another of his former sides, Bayern Munich - the club that he usurped to hand Leverkusen their first ever Bundesliga title last season.
This campaign has not been as favourable for Die Werkself though, as they have taken just 17 points from their opening 10 games, and are nine points behind Bayern, with just one win in their last six.
Alonso also suffered a humbling defeat on his return to Anfield last week, losing 4-0 away to Liverpool in the Champions League, where they are currently in 13th.
Alonso seeking a new challenge?
With his stocks still high, Eurosport Spain claim that "the destination is clear", and he will be the man to replace Carlo Ancelotti at Real Madrid next summer.
Results so far this season at the Bernabeu have left Ancelotti's job under threat, as they are lagging behind Barcelona in La Liga, and have already lost twice in the Champions League.
Both managers have contracts that run until 2026, but it is believed that Ancelotti may depart at the end of season, and the club would have no trouble in getting Alonso onboard to sign.
However, the possibility of Alonso staying in Germany and becoming Bayern's next manager has not been ruled out either.
While Liverpool's punt on Arne Slot has worked wonders so far, the mood is not quite the same in Bavaria, with Vincent Kompany already under pressure at Bayern, despite sitting top of the Bundesliga.
Alonso to take Grimaldo with him?
The report also states that Alonso has revealed to some of the Leverkusen squad that he plans to leave at the end of the season, and that could see some of the players he has built a winning machine with at the club follow him on his new venture.
Grimaldo, despite growing up in and representing Spain, has never played professionally in the country, having left Barcelona for Benfica as a 20-year-old without ever making a first-team appearance.
The left wing-back made a name for himself in the Portuguese capital for his dead-ball ability and impressive attacking returns, but they hit stratospheric levels when moving to Leverkusen last summer.
Arriving on a free, Grimaldo was one of the best performers anywhere on the continent, contributing to 31 goals from wing-back, as Leverkusen completed an unbeaten domestic season.
The 29-year-old's next destination is also unclear at this point, but with Real Madrid's troubles at left-back in particular, due to the form and injury records of Ferland Mendy and Fran Garcia, Los Blancos could be in the market for one next summer.