Ramalho led Sao Paulo to three Brazilian championhips
Brazil have asked Fluminese manager Muricy Ramalho to become their new boss but the 54-year-old is yet to accept.
Ramalho met with the Brazil Football Federation (CBF) on Friday and will now talk to Fluminese officials before deciding whether to take the job.
Brazil are searching for a new coach following Dunga's sacking after their quarter-final exit at the World Cup.
"Nothing is decided because I still have a contract with Fluminese," said Ramalho in a statement.
Dunga and his entire coaching team were dismissed after Brazil were beaten 2-1 by eventual finalists the Netherlands in their last-eight match.
The CBF revealed after Dunga's sacking that a new coach would be installed by the end of July.
Corinthians manager Mano Menezes and former AC Milan coach Leonardo were tipped as possible successors as well as former Brazil coach Wanderley Luxemburgo.
But it appears that the CBF have opted for Ramalho, who led Sao Paulo to three Brazilian championships.
Ramalho has 17 years managerial experience having also played for Sao Paulo. He was never capped by the national side and began his coaching career at Pueblo in 1993.
Brazil host the World Cup in 2014, the first time they have held the tournament since 1950.