Dunga, whose real name is Carlos Bledorn Verri, previously coached Brazil from 2006 to 2010 where he won the 2007 Copa America and the 2009 Confederations Cup. (Agencies)
He was fired by the Brazilian Football Confederation (CBF) after losing to the Netherlands in the quarter-finals of the 2010 World Cup.
One source, who declined to be identified since the process is underway, said Dunga has a good relationship with Gilmar Rinaldi, who was named on Thursday as general manager for Brazil's national teams.
Both players were part of the 1994 World Cup winning team.
The CBF and Dunga, 50, began talks early this week, a second source said.
"He is the front runner in the list and things are moving forward satisfactorily," a second source said.
"There were important meetings that took place in Sao Paulo and Gilmar is fine-tuning details already,” the source added.
A new coach to replace Luiz Felipe Scolari is expected to be named next Tuesday.
Scolari, who guided Brazil to their fifth World Cup title in 2002, resigned as coach after the 2014 tournament where the hosts entered as hot favourites but finished fourth.
They were also humiliated by eventual champions Germany 7-1 in the semi-finals and then lost the third-place playoff 3-0 to the Netherlands.
Both sources dismissed recent local media reports that Tite, who led Corinthians to the World Club Championship in 2012, and Sao Paulo manager Muricy Ramalho were front runners for the job.
Dunga's last job was as coach of Internacional, where he spent a great part of his playing career, but was sacked last October after a fourth successive loss in the Brazilian league that left them mid-table.
As coach of Brazil's national team, he led the team to 42 victories, 12 draws and six defeats.
Dunga, whose real name is Carlos Bledorn Verri, previously coached Brazil from 2006 to 2010 where he won the 2007 Copa America and the 2009 Confederations Cup.