Muricy Ramalho is in line to succeed Dunga as the new coach of the Brazilian national team.
Ramalho currently manages Brazilian outfit Fluminense but was invited by the Brazilian Football Federation to take over from Dunga, who was sacked following the country's quarter-final exit from the World Cup in South Africa.
Federation president Ricardo Teixeira told O Globo TV that he had offered the 54-year-old the job in Rio de Janerio on Friday.
Teixeira revealed any deal would be subject to Fluminense releasing Ramalho from his contract, which runs to the end of the year.
"Now it's up to him to resolve things, taking into consideration that he is under contract to Fluminense," said Teixeira.
Ramalho, who led Sao Paulo to the Brazilian championship in 2006, 2007 and 2008, as well as to the runners-up spot at the Copa Libertadores, was quoted as saying: "Who wouldn't want to coach the Brazilian national team?"
Dunga was relieved of his duties just days after his team lost to the Netherlands in the final eight stage of this summer's tournament, ending his four-year tenure in charge of the Samba nation.
But employing Ramalho as Dunga's heir may prove difficult after Fluminense stated they were unwilling to part company with their manager.
"Muricy is going to continue at Fluminense, fulfilling his contractual commitments," club president Roberto Horcades told reporters.
Reports had suggested the Brazilian authorities were prepared to offer Ramalho a deal up until the 2014 World Cup, which is being staged in the South American country.