Bolasie spent last season out on loan in Portugal with Sporting Lisbon and had been expected to leave Everton again in the last transfer window.
However, he stayed put at Goodison Park, where he is surplus to requirements under Carlo Ancelotti and has not made a competitive appearance this term.
Now Sivasspor are looking to tempt Bolasie, who is out of contract at Everton in the summer, to move to Turkey to rekindle his career.
They have, according to Turkish journalist Ertan Suzgun, made contact with the winger to register their interest.
Bolasie has interest from a number of sides in Europe and it is unclear if Sivasspor can win the chase for his signature.
Everton are keen to offload Bolasie and the winger departing this month would take his salary off the books for the final six months of his contract on Merseyside.
Sivasspor sit in 14th spot in the Turkish Super Lig and have scored just 21 goals from their 20 games so far.