The Sabah newspaper report that Chelsea do not want to loan Remy but want to sell him instead.
Per the source, Besiktas could struggle to sign Remy on a permanent deal due to FFP contraints.
The Istanbul giants will try to find a way around the Blues demands by agreeing to a buyout clause option at the end of the season.
Antonio Conte is not reported to have plans for Remy next season and the Blues are open to offers for the experienced striker.
Besiktas lost star striker Mario Gomez over the summer after he revealed he would not be returning following the end of his loan.
The Black Eagles have made finding a replacement a priority with Champions League football looming.
The Istanbul giants won the league title last season but have lost key players over the summer including Gomez and Gokhan Tore.