The 29-year-old right-winger currently plays for the Spanish side Cadiz.
The Spanish player started his playing career in 2014 in Atlético Madrid C and has also played in Villareal B, Eibar, Getafe and Malaga.
Esteghlal, headed by former Osasuna midfielder Javad Nekounam, had previously shown an interest in signing Alejo and now, Persepolis, who has hired Spanish coach Juan Carlos Garrido, has joined its archrival to try to buy the player.