The Blues are reported to have been scouting the Ghana international in recent weeks and watched Boakye in Thursday's Europa League 0-0 draw against Arsenal at the Emirates Stadium.
Chelsea manager Antonio Conte has just two senior strikers in his squad in Alvaro Morata and Michy Batshuayi, and Boakye, who can also play on both wings, would give him another attacking option.
The 24-year-old has already scored 14 goals in 22 games in all competitions for Red Star this season, form which has brought him to the attention of Chelsea.
Boakye is delighted by the prospect of joining Chelsea, telling Belgrade newspaper Novosti. “I am playing well, so we’ll see who will contact me.
"If I’m going to play for Chelsea, then I’ll go."