Since moving to Stamford Bridge from Newcastle in January 2013, the Senegal international has scored 14 goals in 51 games for the Blues.
He soon fell behind Fernando Torres and Samuel Eto'o in the pecking order, however, and the arrival of Diego Costa from Atletico Madrid this summer has freed him to look for a new club, with Jose Mourinho’s side ready to accept less than their initial £10.3 million asking price.
"The initial price for him was €13m (£10.3m) but we've managed to reduce it," Besiktas chairman Fikret Orman told NTV Spor.
"We'll tell the media once the final deal is done."
Among Ba's most crucial goals for Chelsea were a late strike against Paris Saint-Germain to send them through to the Champions League semi-finals last season, as well as an effort to capitalise on Steven Gerrard's slip at Anfield which spelt the beginning of the end for Liverpool’s title challenge.