PSG announced on Saturday that Mbappe would be staying at the Parc des Princes after agreeing a new three-year deal until 2025, with the forward insisting on Monday that he had been convinced by the club's "sporting project."
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The saga has overshadowed Madrid's preparations for their Champions League final with Liverpool, which will be played in Paris on Saturday.
"With what we have to think about, we've never thought about players from other clubs," Ancelotti said in a news conference. "We respect everyone, we respect the decisions they take, we respect other clubs. But we have to do our jobs, and it's clear what we have to think about now, which is preparing well for the final."
Mbappe, 23, revealed on Monday that he had held talks with both Champions League finalists about a possible move, saying "we spoke to [Liverpool] a bit... but in the end it was between Real Madrid and PSG."
Madrid midfielder Casemiro echoed Ancelotti's comments.
"Everyone takes their own decisions. Everyone does what they want in life," Casemiro said. "If Mbappé wants to stay in Paris, we have to respect that.
"We know this [Madrid] is the best club in the world, the best place to live, but we have to respect his decision, his family's decision, the club, PSG. We wish him the best and let's hope he's happy wherever he is."
Saturday's final at the Stade de France is a repeat of the 2018 showdown, when Madrid beat Liverpool 3-1 in Kiev.
Liverpool's Mohamed Salah -- forced off with a dislocated shoulder in that game -- said he "would prefer Madrid" in the final before the opponent was confirmed, leading Madrid's Federico Valverde to hit back this week accusing Salah of "disrespecting the [Madrid] badge."
"It could be a motivation," Ancelotti said on Tuesday when asked about Liverpool seeking revenge for 2018. "But in the history of Real Madrid there's also a final they lost in Paris against Liverpool [in 1981]. So we could have the same motivation as Salah.
"We respect [Salah], he is a great player, he's dangerous. It could be revenge for them for 2018, or for Real Madrid for the final they lost in 1981."
Ancelotti also has a long history of facing Liverpool -- losing to them on penalties with AC Milan in Istanbul in 2005, before beating them 2-1 in Athens two years later.
"We've met many times," Ancelotti said. "In 2005, a final that it looked like we'd won, we lost on penalties. Then in 2007, and now again. It's a club I respect... I like their history, with Bob Paisley who won three European Cups. It's a historic team and playing a final against them is special."