The 18-year-old wonderkid is one of the most highly-rated teenagers in world football and has already been capped three times by the French national team.
According to The Athletic, Camavinga's refusal to extend his stay could lead to an exit this summer as Les Rennais could risk losing him on a free transfer when his deal expires in June 2022.
Camavinga has been strongly linked with a move to Los Blancos and the midfielder is likely to choose the Santiago Bernabeu over any other club should fellow countryman Zinedine Zidane remain as manager.
United and Paris Saint-Germain are also believed to be monitoring his situation and may approach Rennes this summer if they are made aware of his availability.
Camavinga has played 77 times for Rennes since making his debut as a 16-year-old in August 2019, but the Ligue 1 side are languishing in seventh place in the French top flight and are set to miss out on European football next season.