The report states that Besiktas President Fikret Orman held a meeting with Chelsea representatives yesterday evening and negotiated a €7 million transfer fee for the France international.
AMK go onto state that Chelsea were demanding €10 million but Orman managed to lower the 28-year-old’s price.
Besiktas are on the hunt for a new striker after selling last seasons top scorer Demba Ba to the Chinese club Shanghai Shenhua for €13 million last week.
Remy has found himself on the fridges of the squad after being signed from QPR last summer.
The France international provided two assists and scored nine goals in 29 appearances for the Blues in all competitions. Chelsea won the Premier League last season after amassing 87 points in 38 games.