The Brazilian Football Confederation plan to approach Manchester City manager Pep Guardiola about the Selecao job.
Brazil have sacked Dorival after their 4-1 World Cup qualifying defeat in Argentina this week.
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The CBF are now actively drawing up plans to find a big name replacement for Dorival, with three coaches on their shortlist.
Marca says top of the list is Real Madrid coach Carlo Ancelotti, who was close to taking the job at the end of last season.
Guardiola, who has also flirted with the Selecao, has been added over the past 24 hours. There is a belief inside the CBF that Guardiola could be tempted away given his problems at City.
Meanwhile, the third name being considered is Jorge Jesus, who is currently in charge of Saudi Pro League champions Al-Hilal.