Mourinho had implied Pogba - whose agent Mini Raiola has reportedly been talking with Barcelona - had flourished under Didier Deschamps at the World Cup because he could not be distracted by his entourage or by his commercial obligations.
Mourinho is under increased pressure to deliver success to United after failing to win a trophy at Old Trafford last season.
The 25-year-old was handed the captain's armband for Manchester United's Premier League opener against Leicester City on Friday night and after just three minutes, he bagged from the penalty spot.
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People wave Romanian national flags during a demonstration against the government on Saturday, during the second day of protests. Those changes made it through parliament but are now being challenged in the country's constitutional court.
The two had exchanged tense comments in the media over the summer - primarily with Mourinho urging Pogba to replicate his World Cup form in Manchester.
"We are following many players, Rabiot is one that has shown quality, but time will tell", the advisor said.
Piercing through any sense of satisfaction on an opening day win, Pogba chose to use his post-comments to say, "If you're not happy, you can not give your best". The team had achieved everything it could, numerous players had hit their peak, and the time had come for Zidane to abdicate and allow his successor to guide Real Madrid through their transition period. We're focused on the league, so it's best to ask (Eric) Abidal, (Ramon) Planes or Pep Segura about players.
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The World Cup victor did little to ease the situation after stating that there are things he "cannot say otherwise I will get fined".
This would explain the continuation of the Barcelona speculation, but given that the English transfer window finishing early means that United would not be able to purchase a replacement for Pogba, the chances of him leaving before the end of the month are very slim. "That is the way I think football is going", said Mourinho in an interview with Sky Sports.
Meanwhile, Mourinho was frustrated at the club's failure to bring in extra defensive bodies ahead of the transfer deadline.
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Manchester City's Bernardo Silva celebrates scoring their second EPL goal against Arsenal at the Emirates Stadium August 12, 2018. While that is not something over which Klopp can have an influence over, there are possibly ways the Reds can help themselves.