Despite receiving a strong interest from Brazil since Tite stepped down after the 2022 World Cup, Ancelotti reiterated his desire to continue as coach of Real Madrid until June 2024 when his contract expires.
"He [Ancelotti] is a coach who has this vision and courage to put new talents to play," Rodrigues said.
"No disrespect to any other coach. Brazil has many coaches that we have great appreciation for, and who are competent, but we have a plan, and plan A is exactly that [Ancelotti]."
Rodrigues remains optimistic that he can convince Ancelotti to take over the national team.
"We have the feeling that it can work," Rodrigues said. "Let's wait for the end of the competition [LaLiga], despite already having a champion, Barcelona. But we will wait for the competition to end, and we have the intuition that it can work."
Rodrigues said he understands Ancelotti's contract situation but knows the Italian coach is an admirer of the Canarinha. The Madrid boss already coaches Brazil's attacking pair Rodrygo and Vinicius Junior at the Bernabeu.
"If I were in his place and with a contract in force, I wouldn't belittle the company I was hired for either," he said. "I think he has an enchantment for the Brazilian national team, he knows most of the players who played and who still play for the Brazilian national team."
Rodrigues expects to have a clearer vision of who the next Brazil coach will be in the coming weeks. In the meantime, the CBF are relying on Brazil's under-20 coach Ramon Menezes as interim boss.
"We hope that we can have, right after these games in June, but still within the month of June, a clearer position and that we can speak with greater conditions," he said.
The CBF are also monitoring other Brazil-based coaches, such as Palmeiras' Abel Ferreira, Fluminense's Fernando Diniz and Sao Paulo's Dorival Junior as possible alternatives should they fail to lure Ancelotti.
"The coach will be the one that the CBF understands is the best for the cycle," Rodrigues said. "And this cycle is not just about competing in the World Cup. It's winning the  World Cup."
Brazil have not won the World Cup since 2002.