Varane, 29, had an MRI scan on Sunday after leaving United’s 1-1 Premier League draw at Chelsea with an injury on Saturday. However, the France international sees the diagnosis as a positive one in terms of his chances of helping Les Bleus defend the World Cup in Qatar next month.
The injury leaves France coach Didier Deschamps with a decision to make as Varane is unlikely to be fit for their World Cup opening game against Australia on Nov. 22.
France name their squad for the World Cup on Nov. 9 but countries can replace injured players up to the day before their first match.
Varane rejected the opportunity to leave the pitch at Stamford Bridge on a stretcher, preferring to walk off although he was visibly distressed by the injury to his knee.
The news will be a blow to United boss Erik ten Hag as he looks to challenge for a top-four place in the Premier League ahead of a month-long break for the World Cup.
Victor Lindelof replaced Varane during the game but it also presents an opportunity for out-of-favour England defender Harry Maguire to gain some much-needed playing time and prove his fitness ahead of Gareth Southgate naming his final squad on Nov. 10.
Maguire made a return to training with United last week, having suffered a thigh injury on international duty for England against Germany, and will hope to be in contention for the Europa League game against Sheriff on Thursday.