Carlo Ancelotti is expected to leave Real Madrid in the summer.
Los Blancos have therefore started searching for his replacement.
Their current list contains a former Galactico and a current Premier League manager.
Madrid target De Zerbi and Alonso
Xabi Alonso and Roberto De Zerbi are both targets for the next Real Madrid manager, according to Cadena SER.
For now, the former Real Madrid midfielder is understood to be a step ahead of De Zerbi, but the Italian is also a strong contender.
Alonso has been doing a hugely impressive job at Bayer Leverkusen.
The Spaniard has made the German club one of the most exciting teams to watch and a contender for the title in the Bundesliga.
Leverkusen are currently 2nd in the German top flight having made an unbeaten start, which includes a draw away at Bayern Munich.
Meanwhile, De Zerbi is doing an equally impressive job at Brighton.
Last season, he helped the Seagulls qualify for Europe for the first time ever and this season, his team are 3rd after six matches.
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