Carlo Ancelotti said he hopes Xabi Alonso can coach Real Madrid "one day" after the Bayer Leverkusen boss was linked with the position following Real's 3-1 derby defeat to Atletico Madrid on Sunday.

Alonso, 41 -- who twice played for Ancelotti, including at the end of a five-year spell as a Madrid player between 2009 and 2014 -- has guided Leverkusen to second in the Bundesliga this season, level on points with league leaders Bayern Munich.

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ESPN reported in May that Alonso is the leading candidate to take over from Ancelotti, whose contract at the Santiago Bernabeu expires in June 2024.

"I had Xabi Alonso as a player," Ancelotti said in a news conference on Tuesday ahead of Madrid's LaLiga game with Las Palmas. "He has a high-level knowledge of football. He's doing very well with Bayer Leverkusen. He has that reading [of the game], that capacity.

"I think one day -- for Raul [Gonzalez], for [Alvaro] Arbeloa, for Xabi Alonso -- their biggest wish is to coach Real Madrid and I want that for them because I know them all, I love them all. Let's hope that one day they can be Real Madrid coaches."

Alonso starred for some of modern football's top managers -- Rafa Benitez, Jose Mourinho, Ancelotti and Pep Guardiola -- as a midfielder at Liverpool, Real Madrid and Bayern Munich, before beginning his coaching career at Madrid's academy.

He spent three seasons in charge of boyhood club Real Sociedad's reserve team before taking over at Leverkusen in October 2022, taking them from a relegation battle to Europa League qualification.

Ancelotti faced criticism for his team selection and tactics in Sunday's LaLiga loss to Atletico after leaving forward Joselu out of the starting eleven and picking Jude Bellingham in attack alongside Rodrygo, with Luka Modric and Toni Kroos in midfield.

"[Criticism] is part of the job of a coach," Ancelotti said. "When you're Real Madrid manager, it's normal that you get criticism when things don't go well... I have to evaluate, in a self-critical way, what we've done, what we're doing well, which is a lot, and what we didn't do well against Atletico Madrid.

"I have to evaluate things with balance," he said. "Fortunately that's in my genes, I'm a balanced person. It isn't that difficult. It isn't about doubting everything. The team had won six games out of six, with all the [injury] problems we've had."

Ancelotti has ditched his usual 4-3-3 formation this season, opting to use a midfield diamond to get the best out of Bellingham and compensate for his lack of attacking options.

However the team's defence was left exposed against Atletico, with all three goals coming from headers -- two from Álvaro Morata and one from Antoine Griezmann -- after crosses into the box.

"Every system has its weakness," the Italian said. "The midfield diamond isn't perfect, neither is 4-2-2 or 5-3-2... This [formation] allows us to press more, with more energy to win the ball back, but the weakness is sometimes [the opponent] can find you out of position when they cross, because the midfielders don't always have time to get back and help the defence. When something is clear, you can fix it."