The Turkish outfit are hoping to bring the German in on loan for a season.
The talented young striker is being targeted by Turkish side Trabzonspor, according to a report in Haber Turk.
They claim that Liverpool want to send the player out on loan to Turkey in order for him to get plenty of regular first-team football.
German striker Yesil, who is off Turkish descent, has been linked with Trabzonspor before. Almost exactly a year ago in fact Sky Sports reported that Yesil was keen on a move to the Turkish outfit.
Liverpool snapped up Yesil in 2012 from Bayer Leverkusen and were getting their hands on one of the top talents in German football.
However he has had a torrid run of injuries during his time at Liverpool. Not long after playing his second game for the first-team in the League Cup he suffered a knee ligament injury on international duty. He then suffered the injury again and he has effectively been out of action for the past two years.
A loan spell might just be the perfect opportunity for him to prove to Liverpool he has what it takes to make it in the Premier League.