Carlo Ancelotti has won the Champions League four times as a manager and twice with Real Madrid
The five-time World Cup winners are confident the Italian will be in place for the Copa America in June 2024.
Rodrigues said Fernando Diniz will oversee the Selecao until then, alongside his role as Fluminense boss.
"He will come and make the transition in Brazil for Ancelotti," Rodrigues said.
"His game plan is almost similar to that of the coach that will take over at Copa America, Ancelotti.
"We don't call him an interim coach of the national team."
Brazil have been without a permanent head coach since the World Cup, when Tite resigned following their quarter-final defeat by Croatia, with under-20s coach Ramon Menezes taking charge of recent friendly fixtures.
Ancelotti, whose contract expires next summer, would be the first foreign manager to coach Brazil since 1965. There has been no official word from Ancelotti or Real Madrid that he will depart the club next year.
The 64-year-old began his second spell at the Bernabeu in 2021, after leaving Everton, and has won the Champions League, La Liga, a Copa del Rey and the Club World Cup among a string of successes since his return.
The Champions League final win against Liverpool in 2022 was Ancelotti's fourth European triumph as a manager, and second with Real Madrid, after also winning the competition twice with AC Milan.
-- Courtesy of BBC Sport