A group of France stars were seen arguing on the pitch during the match and things got worse after the defeat as the World champions were dumped out of the competition.
Pogba helped put France 3-1 ahead 25 minutes before the end in the last-16 clash.
But some of his teammates were reportedly unhappy with the lack of defending he was doing on the night.
"Benj (Pavard) thinks that you are not defending enough," Varane is said to have told Pogba, according to Le Parisien.
A furious Pogba is then said to have confronted Pavard to ask: "What did you say?"
Pavard allegedly continued with several insults as the row escalated. Tension eventually eased and Pogba later apologised to Varane.
Real Madrid defender Varane is now a top transfer target for Pogba's United.
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