The experinced manager wants to replace the out-bound Oscar Cardozo with the young striker whose contract expires with the Red’s this summer.
Yesil is understood to be keen on a move to the Turkish Super League after struggling with injuries over the past two seasons.
The 22-year-old will leave the Merseyside club on a free transfer this summer according to the Liverpool Echo.
The daily Liverpool based paper state that the 22-year-old is out of contract and has not been offered a new deal by Reds.
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.
The 22-year-old has made two assists and has found the back of the four times in 17 appearances for Luzern this season.