Brazil are yet to name a successor to Tite, who stepped down after the Selecao's quarterfinal elimination at the 2022 FIFA World Cup in Qatar.
Ramon Menezes took temporary charge of Saturday's 2-1 friendly defeat to Morocco.
Ancelotti is contracted to Real Madrid until the summer of 2024 but his experience of working with some of Brazil's key players makes him a wise choice.
CBF President Ednaldo Rodrigues has admitted players and fans alike are clamouring for the four-time Champions League winner to be given the hot seat.
"Ancelotti is unanimously respected among players. Not only Ronaldo Nazario or Vinicius Jr but all those that have played for him," he told Reuters.
"I really admire him for his honesty in the way he works and how constant his work is. He needs no introductions. He is really a top coach who he has several achievements, and we hope he can have even more.
"Ancelotti is not only the players' favourite, but it seems the fans' too. Everywhere I go in Brazil, in every stadium, he is the first name the supporters ask me about.
"They talk about him in a very affectionate way, in recognition of the exemplary work he has done in his career.
"Let's have faith in God, wait for the appropriate time and we'll see if we can make it happen as we look for the new coach of the Brazilian national team."
