The 28-year-old joined the Blues in 2016 and his contract with them runs out at the end of the season.
Batshuayi has had five loan spells while at Chelsea, with stints at Borussia Dortmund, Valencia, twice at Crystal Palace and Besiktas.
He looked set for a move to Nottingham Forest but it fell through on Thursday's transfer deadline day.
Fenerbahce say Batshuayi is scheduled to travel to Istanbul to complete the move.
