Derakhshan replaced Ali Daei in September but was forced to quit after poor results.
With six weeks remaining, Persepolis currently is ninth in the Iran Professional League (IPL).
The Iranian popular team will host Al-Nasr of Saudi Arabia on Wednesday in Group A of the AFC Champions League in Tehran’s Azadi Stadium.
Persepolis assistant coach Hossein Abdi has been named as interim coach.
Former Iran coach Branko Ivankovic is a candidate to take charge Persepolis.