The 21-year-old has been granted permission by the French side to undergo a medical with the Black Cats ahead of signing a five-year-deal, per David Ornstein of The Athletic.
The deal is reportedly worth £25.7 million, plus an extra £4.3m in potential add-ons.
It is believed the paperwork is still to be completed, but the deal is on ahead of Tuesday's deadline.
Flashscore had reported that Arsenal were debating whether or not to pay Lyon's asking price for the winger, who was offered to them in the days leading up to the end of the transfer window.
Fofana would join Thomas Meunier, Dayann Methalie and Jules Ahoka to become Sunderland's fourth summer signing - although a deal is also expected to go through for Tottenham defender Kevin Danso.
The wide man has scored twice in six appearances for Lyon this season, and has scored 19 Ligue 1 goals in total over the course of two-and-a-half years.
Fofana will now play his football under manager Regis Le Bris as Sunderland prepare for Europa League action this season.