The Sun says the French midfielder did not start the derby clash after being dropped by United's Norwegian boss on Sunday and while he did come on at half-time, he was sent off 15 minutes into the second half for a high lunge on Liverpool's Naby Keita.
Pogba apologised to his team-mates for his red card at Old Trafford, though did not say anything to Solskjaer after the loss.
The reported snub raises questions over Pogba's future at Old Trafford, with the 28-year-old's contract at Manchester United expiring at the end of this 2021-22 season.
Pogba's agent Mino Raiola has insisted that there is 'no update' in regards to the midfielder's ongoing contract situation.
If Pogba fails to agree to an extension before January, he will be allowed to discuss terms and sign a pre-contract with a foreign club ahead of a move next summer.
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