The Belgium international joined Chelsea from Ligue 1 club Marseille for a fee in the region of £35m in 2016, but has struggled to make an impact at Stamford Bridge.
Following his move to Stamford Bridge five years ago, the 27-year-old has spent time on loan at Bundesliga side Borussia Dortmund, La Liga outfit Valencia and Crystal Palace.
Batshuayi, who has struggled to find his footing at Chelsea as well as his three loan clubs, has entered the final year of his contract with the Blues.
As the centre-forward continues to be linked with a move away from Stamford Bridge, Turkish club Trabzonspor have emerged as an option for him this summer.
According to Turkish outlet En Son Haber, Trabzonspor have identified Batshuayi as a potential candidate to solve their goalscoring problems next season.
The Turkish Super Lig club are said to have touched base with Chelsea to enquire about the possibility of signing the Belgian frontman this summer.
Trabzonspor have identified RB Leipzig striker Alexander Sorloth as their priority target, but view Batshuayi as an alternative should they not be able to sign the Norwegian.
While it remains to be seen if Trabzonspor will step up their interest in Batshuayi, the 27-year-old is said to be open to a move to Turkey this summer.