The 25-year-old player has traveled to Tehran to finalize his contract with the Blues.
Mame Baba Thiam started his playing career at Italian giant Inter Milan in 2011 and has also played at Avellino, South Tyrol, Lanciano, Juventus and Empoli.
Esteghlal also completed the signing of Macedonian central midfielder Bojan Najdenov on Monday.
The Blues are going to strengthen for the 2018 AFC Champions League.
Esteghlal has been drawn along with Al Rayyan of Qatar, Al Hilal of Saudi Arabia and Al Ain of the UAE in Group D of the competition.
Esteghlal will meet Al Rayyan of Qatar on Feb. 13 in Doha in its opening match.
Winfried Schafer’s team also sits sixth in Iran Professional League, 19 points behind pacesetter Persepolis.