The 29-year-old, who has 93 caps after making his debut in 2013, and also helped Didier Deschamps's side win the UEFA Nations League in the 2020-21 season.
Since the departure of Cristiano Ronaldo to Al Nassr, Manchester United are set to introduce a squad-wide salary cap in order to avoid jealousy among players.
Centre back Varane, 29, went over his ankle midway through the second half in Sunday's 1-1 draw with Chelsea and looked distraught as he made his way into the tunnel at Stamford Bridge.