The defender will leave Fulham when his contract expires at the end of the month.
Advertisement
Advertisement
Adarabioyo had also fielded interest from Newcastle and Manchester United, but is now a step away from signing for Chelsea.
Sky Sports says a medical is being organised for this week.
Chelsea are said to be the "clear favourites" for Adarabioyo's signing, but will stay "cautious" until the deal is completed.