The former Bolton and Fulham midfielder is without a team after parting company with Qatari side Umm Salal.
Teymourian scored a wonderful long-range goal against Buriram in Esteghlal’s 2-1 win over the team in the 2013 AFC Champions League.
Iranian media suggest that Esteghlal also wants to strengthen its squad by signing Ando.
The 32-year old midfielder joined Umm Salal but left the club halfway through the season after a disagreement with the head coach and with only 12 appearances and no goals.