The lead candidate to lead the Selecao is Dunga -- who was sacked after losing in the 2010 World Cup -- according to a report by Reuters.
Luiz Felipe Scolari stood down this week after the hosts could only finish fourth at the World Cup, having been thrashed in their semifinal 7-1 by eventual winners Germany, and then beaten 3-0 by Netherlands in the third-place playoff.
The announcement comes on the back of the appointment on Thursday of Gilmar Rinaldi as Brazil's general coordinator, with responsibility for all levels of the national team.
Rinaldi and Dunga have a good relationship, having both played on the 1994 World Cup championship team.
"The president of the CBF, Jose Maria Marin, will present the new coach of the Brazilian national team at a news conference at 11 am this Tuesday,'' read a statement on the CBF's website.
Reuters' sources reputed reports that Corinthians boss Tite and Muricy Ramalho of Sao Paulo were also front-runners. Another former boss in Vanderlei Luxemburgo is also thought to be in the reckoning.
"We've talked about some things and we are in contact,'' said Rinaldi as he was unveiled in his new post. "The most important thing is to define what we want and the profile of the person we want. We must recognise that we need to change.''
Carlos Alberto Parreira also left his post as technical director following the World Cup along with Scolari's backroom staff.
Information from Press Association was used in this report.