The Italian has a contract at Bernabeu until the summer of 2024, but there has been a host of talk surrounding a move away from the Spanish and European champions at the end of the season.
Brazil have identified Ancelotti as their leading target to replace Tite as head coach, with CBF president Ednaldo Rodrigues recently confirming the interest.
"I am not saying Ancelotti has an offer from us, but we are checking if he wants to come. We have a plan A and I say it for the first time honestly. There is no point in hiding this, he is the favourite," Rodrigues said.
Real Madrid are set to relinquish the La Liga title to Barcelona, with the Catalan outfit now on the verge of winning the championship, currently sitting 14 points clear of third-placed Los Blancos in the table.
Ancelotti delivered yet another trophy on Saturday night, though, with the capital outfit recording a 2-1 victory over Osasuna in the final of the Copa del Rey.
Real Madrid are also chasing success in the Champions League this season, preparing to welcome Manchester City to Bernabeu for the first leg of their semi-final on Tuesday night.
Perez was asked about Ancelotti's future in the aftermath of the Copa del Rey final success, and the club's president said that the Italian would be staying as head coach for next season.
"I don't even want to hear about that. We have one more year on his contract. We are very happy with Ancelotti," Perez told reporters on Saturday night.
Ancelotti won three competitions for Real Madrid during the 2021-22 campaign, with Los Blancos triumphing in La Liga, the Champions League and the UEFA Super Cup.
The 63-year-old is currently in his second spell in charge of the capital giants, and he has won one La Liga title, two Copa del Rey trophies, the Spanish Super Cup, two Champions League crowns, two UEFA Super Cups and two Club World Cups during his time at the helm.
Ancelotti recently said that he was "very excited" by Brazil's interest, with the experienced head coach said to be open to managing the South Americans in the future.
Ramon Menezes - head coach of Brazil Under-20s - is currently in charge of the senior side on an interim basis, replacing Tite, who left his role following a disappointing 2022 World Cup.
Real Madrid will welcome Man City to Bernabeu on Tuesday evening for the first leg of their Champions League semi-final, before returning to La Liga action at home to Getafe next weekend.