The 22-year-old’s agent has met with Trabzonspor’s representatives in Turkey however, Besiktas have also expressed an interest in the Germany u19 international.
The Black Eagles made a late move to sign Tolgay Arslan from HSV ahead of Trabzonspor and Besiktas over the January transfer window.
Yesil is expected to leave Liverpool at the end of June when his contract is set to expire.
The former Bayer Leverkusen man joined Liverpool from Bayer Leverkusen for £1 million and has gone onto make just two appearances for the Reds.
Yesil has made two assists and has found the back of the four times in 17 appearances for Luzern this season. The young striker has also made seven appearances for the Germany u19 side.
The Black Eagles won the league title this season and would be able to offer Yesil Champions league football.