Pogba came on as a half-time substitute only to endure a nightmare 15 minutes, as his error led to Liverpool's fifth goal before he was shown a straight red card for a horrendous challenge on Naby Keita.
The midfielder surrendered possession to Jordan Henderson, who in turn played the ball through for Mohamed Salah to complete his hat-trick. Then, his challenge on Keita saw the Guinea international leave the pitch on a stretcher.
The World Cup winner did apologise to his teammates following the reckless challenge, but did not communicate with Solskjaer.
Pogba was reportedly considering the possibility of signing a new contract at United, but those talks are now on hold.
The Frenchman's current deal at Old Trafford expires in June 2022, meaning he will be able to speak with other clubs in January and leave as a free agent next summer.
The Sun report explains that the 28-year-old's outspoken comments in the aftermath of United's 4-2 defeat at Leicester City did not sit well with Solskjaer.
"We've had these kinds of games for a long time," he said.
"We have not found the problem, conceding easy goals - we need to be more mature, play with more experience and arrogance in a good way.
"We need to find something; we need to change."
Pogba has fallen out of favour in recent weeks, and was left out of the dramatic 3-2 Champions League victory over Atalanta before Sunday's match against Liverpool.
He is also yet to find the net this season in 12 appearances across all competitions, but did register seven assists in his first four Premier League games. This included four in one game, as United thrashed Leeds United 5-1 on the opening day of the season.
But after experiencing a renaissance in his form, Pogba now appears to have dropped down the pecking order in these troubling times at Old Trafford.
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