As speculation over Menezes' eventual replacement increased, Andres Sanchez, the CBF's national teams director and a friend of the coach, said he was not consulted over Friday's surprise firing and was likely to abandon ship.
Brazil's 2002 World Cup winner Luiz Felipe Scolari, Corinthians coach Tite and Santos coach Muricy Ramalho are considered the favourites to take over, however the name of former Barcelona coach Pep Guardiola is also gaining momentum.
Brazil has never had a foreign coach and the idea was unthinkable until recently. However, the idea has been well received by the media.
The decision is expected in January, just six months before Brazil hosts the Confederations Cup which is a dress rehearsal for the following year's World Cup in the country.
"I haven't been fired or resigned but the likelihood is that I will [resign]," Sanchez told reporters at the Soccerex conference on Monday.
"The sacking came at a very bad moment. It's not a crisis but it creates insecurity. We are three or four days away from the Confederations Cup draw and we don't have a coach."
Sanchez said he was not consulted about Menezes' sacking and that there was no vote among the CBF leadership.
CBF president Jose Maria Marin addressed the Soccerex conference during its opening ceremony but made no mention of the coach's situation.
Instead, he spoke of potential improvements to stadiums and infrastructure that would be provided when Brazil hosts the World Cup.
Surrounded by security guards as he arrived, the 80-year-old would say nothing other than to repeat that a new coach would probably be picked in January.
Menezes was fired just as he seemed near to finding his ideal team after two years of experimenting.
The five-times world champions have won six of their last eight games, scoring 26 goals in the process, and the Brazilian Football Confederation (CBF) admitted the decision had little to do with results.
