"The name of the new coach will be known between Friday and Monday," CBF spokesman Rodrigo Paiva told reporters.
The favourites to occupy one of football's hottest seats include Luiz Felipe Scolari, who led Brazil to their fifth World Cup title in 2002, Corinthians coach Mano Menezes, Fluminense's Muricy Ramalho and Abel Braga, who is coaching in the United Arab Emirates.
Ramalho (pictured) won three consecutive Brazilian championship titles with Sao Paulo while Braga won the South American Libertadores Cup and World Club championship with Internacional in 2006.
Menezes made his name when he led Corinthians, one of Brazil's most popular clubs, out of the second division in 2008 and guided them to the Copa Brasil title the following year.
With Brazil hosting the 2014 World Cup, pressure to win a sixth title will be more intense than usual.
Brazil were knocked out of the 2010 finals in South Africa by the Netherlands in the last eight and Dunga and his entire coaching staff were sacked just two days later even though the coach had announced he would not stay on in the job.
Dunga won the Copa America and Confederations Cup in his four-year stint at the helm but was criticised for his team's lack of style and finesse.
Brazil's next match is a friendly away to the United States next month.
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