Yesil has seen his time at Liverpool blighted by injury after suffering two serious cruciate knee ligament injuries which kept him out of action for almost a year.
The 20-year-old joined Liverpool in the summer of 2012 from Bayer Leverkusen and was tipped as one for the future at Anfield, but due to injuries he has only made two appearances in the first team.
Liverpool are thought to be willing to loan out the Germany Under-19 international and Yesil claims he is flattered to be linked with Trabzonspor even though he is in no rush to leave Anfield.
"Trabzonspor have made an offer to Liverpool," Yesil is quoted as saying by TurkishFootball.com.
"However, I have not entered talks with Trabzonspor yet. It's an honour to be associated with Trabzonspor but I don't want to leave Liverpool either."