The 22-year-old has been closely linked with a move to the Black Sea based club for the past four seasons.
“I have received offers from Trabzonspor for the past four years. I would like to join the club for the 50th year anniversary,” Yesil was quoted as saying by Super Haber.
The former Bayer Leverkusen player is known to be a Trabzonspor fan and spent his summer break in the Black sea region of Turkey.
Trabzonpor are looking to re-build their squad for the upcoming season following a disappointing year. The 2016-17 season will be Trabzonspor’s 50th year anniversary and the clubs President is targeting the Turkish Super Lig title.
Yesil is expected to leave Liverpool at the end of June when his contract is set to expire.
The 22-year-old has made two assists and has found the back of the four times in 17 appearances for Luzern this season.