Pogba has cut a glum figure on his return to Manchester after France's triumph at the World Cup, but Mourinho insists the midfielder "wants to stay".
"I can only comment on what is real for me, and not on what I read or what I listen to," said the Portuguese.
However, Pogba said he would be fined if he discussed his true feelings after the opening day victory over Leicester.
The Frenchman fell out of favour at Old Trafford during an indifferent 2017-18 campaign for the 25-year-old.
But following some inspired performances in Russia, including a goal in the World Cup final against Croatia, Pogba has been linked with a move to Barcelona this summer.
Speaking before France's Nations League match against Germany this month, Pogba said: "My future is currently in Manchester. I am playing there at the moment, but who knows what will happen in the next few months."
However, Mourinho has since dismissed those comments, saying it is the "player's problem and his relation with the media".