The Senegal international moved to Chelsea from Newcastle United in January 2013, but has largely struggled to produce his best form at Stamford Bridge.
Besiktas chairman Fikret Orman has said that the Premier League club wanted in the region of £10m for the forward, but that figure has now been reduced.
"The initial price for him was €13m (£10.3m) but we've managed to reduce it," Orman told NTV Spor.
"We'll tell the media once the final deal is done."
The 29-year-old scored eight times for Chelsea last season.