Pogba played a crucial role for Didier Deschamps' triumphant side in Russia, and the 25-year-old star returned to United training on Monday ahead of Friday's opening Premier League fixture of the season against Leicester City.
La Liga champions Barca are reportedly interested in taking Pogba to Camp Nou, with the transfer window still open until August 31 for most of Europe's major leagues, while former club Juve have also been linked.
However, United had no intention of letting the midfielder go, a point manager Mourinho affirmed, though he added that the Frenchman may not feature against Leicester at Old Trafford.
"My perception, he arrived Monday, happy, proud, a desire to work," Mourinho told a press conference.
"He worked amazingly well Monday, Tuesday, Wednesday. He's one of the players that I have to speak to, to see how physically and mentally he feels.
"But it's the same conversation as with [Ashley] Young, [Marouane] Fellaini, [Jesse] Lingard, it's the same.
"If they feel they can help us [against Leicester] – 20 minutes, 10 minutes, half an hour. We don't have many solutions and want to go with everything we have.
"I see [Pogba] very well but we need words with that small group to see if they can give us a hand. We have to try and get the best out of every player."
Mourinho was left frustrated in his attempts to bolster United's squad ahead of the season, as the club failed to bring in a central defender, with a late bid for Atletico Madrid's Diego Godin proving fruitless.