The 27-year-old has scored 25 goals in 77 appearances for his parent club in all competitions and has a contract with the Blues until next June.
The Belgium international has spent the 2020-21 campaign on loan with Crystal Palace, though, finding the back of the net twice in 18 Premier League appearances.
According to Ajansspor, Trabzonspor are keen to bring the centre-forward to Turkey in the upcoming market.
The report claims that the Super Lig outfit are hopeful of agreeing a loan move with an option to buy, although the deal would be complicated by the fact that the Belgian is out of contract at Stamford Bridge next summer.
Batshuayi joined Chelsea in 2016 after a strong spell with Marseille but has largely struggled to make his mark for the capital outfit and does not appear to have a future with Thomas Tuchel's side. body check tags ::