Pogba, 23, became the most expensive footballer of all time when moving to United from Serie A champions Juventus for £93.8m earlier this month.
All eyes will be on Pogba, who left United to join Juventus in 2012 before returning this summer, when he makes his second Premier League debut for the Red Devils against Southampton on Friday.
However, while big things are expected from Pogba following his world record transfer, Mourinho insists he does not believe a huge amount of goals should be one of them.
"Can Paul score Ronaldo and Messi's goals?" Mourinho said. "Not even 25 per cent, I believe. I believe he cannot score 20 goals in a season.
"So if to be the best player in the world means to score a lot of goals, that's not the point. But he's one of the best midfield players, maybe I could say the best midfield player, in the world.
"I'm not worried with an 'impact' and I don't think he's worried with that. I see him very calm, I see him very comfortable in this role of a star player and feeling very well under that skin.
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"I don't see him under pressure, I don't see him in training trying to do things to show that he's different, to show that he's better.
"I think his impact will be something very natural, a progressive impact of contribution to improve the team, because that's what he's here for - to win trophies.
"I'm not expecting, the first time he touches the ball, to dribble past five guys and score a wonder goal. I expect the first time he touches the ball to make a correct pass, a good selection of passing, a good choice, a good simple execution and a fluid game.
Mourinho added: "So, maybe it's not an impact, maybe just a natural improvement of the team, because he's a super football player.
"When you speak about the best players in the world, you go immediately to the ones that score a lot of goals.
"You don't give a golden ball [Ballon d'Or] to a goalkeeper. You gave it to [defender Fabio] Cannavaro once, because in that season he was the captain of Italy, the world champions.
"[Paolo] Maldini never got a gold ball. [Javier] Zanetti never got a gold ball. Top goalkeepers, over history, didn't get a gold ball. You look immediately to the ones that score a lot of goals."