Taghavi, 48, worked as Tractor interim coach in 2019 and is without a team at the moment. He was an Esteghlal player from 1993 to 2000.
Fekri, who currently leads Nassaji, also is a candidate to take charge of the Blues.
He was a member of Esteghlal club in two stints.
Foolad coach Javad Nekounam and ex-Esteghlal coach Farhad Majidi were also candidates but media reports say that they have little chance of being appointed as Esteghlal coach.