Iranian media reports suggest that the officials of the giant football club will meet Branko on Monday in Istanbul, Turkey.
Branko was appointed as Iran football coach in 2002 and led the team to 2006 World Cup, but was sacked after the Persians failed to advance to the group stage.
Former Iran and Persepolis coach Afshin Ghotbi is also shortlisted for the job.
Persepolis currently is 9th in Iran Professional League (IPL), 14 points behind leader Naft.
The team will participate in the AFC Champions League.