According to French sports newspaper L'Equipe, midfielder Pogba is unhappy with the more defensive position in which he has been used by Mourinho.
Pogba, who rejoined United from Juventus for £89.3 million ($123.5 million, 100.5 million euros) in August 2016, has struggled in recent weeks and Mourinho has taken the 24-year-old off during two of the Red Devils' last three matches.
Other reports said the arrival of Alexis Sanchez has unsettled the Frenchman.
At his press conference on Friday, ahead of the FA Cup fifth round tie against Huddersfield, an irate Mourinho said Pogba would play on Saturday and dismissed suggestions there was any issue between him and the France international.
"I accept and I can speak on Paul’s behalf without any kind of problem. Paul accepts that he has not been playing well in the last few matches but that's all.
"I don't have to speak with you about my conversations with my players. I don't have to tell you anything about it," the Portuguese boss added.
"It's my problem, it's the player's problem. It's a big lie that the relation is not good, a big lie that we don't communicate, a big lie that we don't agree with his positions and his involvement in the dynamic of the team."
'Their surname is Liar'
Mourinho admitted that in the last two matches Pogba "did not play well" but he told the press conference: "I think you are nice with your words, because when you say 'a lot of speculation' you should say 'a lot of lies'."
"There are people in your role that their surname is 'Liar'."
Mourinho, whose second-placed side are a huge 16 points behind runaway Premier League leaders and local rivals Manchester City, believes Pogba's difficulties in overcoming hamstring and thigh injuries sustained in September have contributed to his struggles.
"He had a big injury in the season, a big injury," Mourinho said. "He was out for a long long time. And in this moment he is not playing well, period. He is not playing well, period. And the team needs him at a good level.
"And when he is not playing at a good level the team is not as good as the team can be. I think it happens with every team when the best players, the most crucial players, for some reason are not performing. Period."
Mourinho also said there was no disagreement between him and Pogba about the player’s position as he again rounded on those in the media who have questioned how the midfielder is used.
"Do you know which is the Pogba preferred system? 4-3-3. Do you know which is Pogba's favourite position in the 4-3-3? No.8 on the left," Mourinho said.
"I would like someone to tell me in which position, Pogba played against Newcastle. Does one of you want to tell me?
"We played with one no.6 and two no.8s. We played with (Nemanja) Matic as a no.6, (Jesse) Lingard on the right side of Matic and Pogba on the left.
"So it's easy and honest, and objective to say Paul Pogba did not play well against Newcastle. But some of the guys (reporters)are paid millions.Don't let people read things that are not true. You are paid to read the game, to explain (to) people the game. Don't say bullshit."