A source close to Turkish-football.com revealed that Remy is on the Black Eagles shortlist along with four other strikers including Liverpool forward Christian Benteke and last seasons loan star Mario Gomez.
Remy has not featured for the Blues over the pre-season and has been instructed to find a new club.
There is however, a slight caveat as the Blues could end up including Remy as part of the deal to sign Romelu Lukaku from Everton.
Besiktas are yet to sign a replacement for Gomez who finished last season as top goal scorer and played a key role in winning the league title.
The experienced striker ended up earning a place back in the Germany national team as a result of his efforts and scored twice over the course of Euro 2016.
Remy scored just one Premier League goal last season for the Blues in 13 appearances, most of which were off the bench.