Per the source, the Black Eagles want the France international striker on loan and the Blues are reported to keen on the 29-year-old leaving.
The Istanbul giants have submitted there offer and expect Chelsea to make a decision within the next 48 hours.
Besiktas are running out of time to sign a replacement for Mario Gomez who did not return after his loan deal ended.
Gomez finished last season as top scorer with 26 goals and played a key role in the Eagles winning the league title to guarantee a Champions League spot.
Remy still has another two-years remaining on his contract but Antonio Conte has now plans for him this season. The experienced striker struggled to settle in over the last league campaign managing to scored just one goal.
Galatasaray – 2016-17 Season Preview