Per the source, the Black Eagles want Remy on loan and talks have reached an advanced stage.
The Istanbul giants are running out of time to find a replacement for Mario Gomez going into the Champions League campaign.
Gomez scored 26 times last season and played a key role in winning the league title, earning himself a recall to the Germany national team in the process.
Chelsea boss Antonio Conte has dropped Remy from the team and has not included the France intentional in his last two games.
Remy was not in the match day squad today that beat Watford 2-1 on the road.
Chelsea XI to play Watford: Courtois, Ivanovic, Cahill, Terry, Azpilicueta, Kante, Matic, Pedro, Oscar, Hazard, Costa
Subs: Begovic, Aina, Loftus-Cheek, Fabregas, Chalobah, Moses, Batshuayi.
Remy has 31 caps for France scoring seven times since his debut against Nigeria in 2009. The 29-year-old also has experience playing for sides challenging for the league title and has played Champions League football.
Besiktas – 2016-17 season preview