The Turkish side's boss has hinted that he would like to sign his former protege from their time at FC Seoul, with the Trotters resigned to losing their players after relegation.
The 23 year old midfielder endured a torrid 2011-12 season, breaking his leg in pre-season before appearing as a substitute in the final two games as Owen Coyle's side suffered relegation on the final day.
The pair know each other well from Gunes' time as manager of FC Seoul from 2007-09, where he handed Lee his debut with the club.
Lee joined Bolton from Seoul in 2009 in a deal worth €2.5 million (£2m), and has one year left on his contract.
And the 59 year old, who steered Trabzonspor into the Champions League last season, hinted that a future move to Turkey could materialise.
"Lee Chung-Yong has always been like a son to me. I will explore all the possibilities to sign him." the former Turkey boss told reporters at Incheon Airport, after visiting the Yeosu World Expo to promote his native country.
"I will contact him while I stay in Korea."
Trabzonspor ended the Super Lig campaign in third place, and will enter the Europa League in the play-off round.