The Turkish giants are reported to have made their first contact with the 24-year-old Fiorentina striker after he was recommended to the side by former forward Demba Ba.
Following unsuccessful pursuits of Gignac, Olivier Giroud, Diego Costa, Besiktas turned to Ba for advice and the 32-year-old looked no further than his Serie A based compatriot.
According to Fotomac, the Black and Whites have since entered the market in search of the 1.85m tall attacker.
The publication also understands that Besiktas and Babacar are expected to meet in a few days.
Babacar's current deal with Viola runs until 2019 but Senol Gunes' men are reported to have prepared about 8 million euros for the Thies-born forward and will use Ba as an intermediary in this transfer.
Ba, who believes he can convince his compatriot was quoted saying:
" Pepe is coming and Besiktas will be in the Champions League this year and that Khouma will pay attention".
However, Besiktas are not alone in the race to sign the Lions of Teranga international who scored 14 goals in 31 matches last season as there are claims that West Bromwich and Crystal Palace also in pursuit of the player.