The five-time World Cup winners have spent the duration of 2023 searching for a new manager after Tite left his role following the 2022 World Cup.
Ancelotti has been continuously linked with the position over the last few months, and Brazil were confident of appointing the Italian.
However, the Real Madrid manager has attempted to play down the speculation, maintaining his position that he will be at the Santiago Bernabeu this season.
Despite Ancelotti publicly making his stance clear, The Athletic are reporting that the Brazilian FA (CBF) still want to appoint Ancelotti as their new permanent head coach.
The report claims that Ancelotti remains their first choice, and they believe that they can convince the 63-year-old to take on the role.
CBF president, Ednaldo Rodrigues, has previously set a deadline of May 25 to decide on the next coach, but Brazil are prepared to give themselves more time to persuade Ancelotti.
As a result, interim boss Ramon Menezes will remain in charge for next month's friendly fixtures against Guinea and Cameroon.
The CBF have considered a number of alternative candidates, including Roma boss Jose Mourinho, who has been linked with the manager's position at Paris Saint-Germain.
Fenerbahce's Jorge Jesus, Fluminense's Fernando Diniz and Palmeiras's Abel Ferreira are all believed to be on Brazil's radar.
Ancelotti, meanwhile, is coming towards the end of his second season with Real Madrid after he returned to the Spanish giants in 2021.
The Real Madrid boss has won five trophies in his second spell with the club, including the La Liga title, the Champions League and the Copa del Rey.
Los Blancos will attempt to wrap up second place in La Liga when they face Athletic Bilbao in Sunday's final league game of the season.