The midfielder is aiming to win the Premier League, FA Cup and Europa League this season, saying: "I want everything. That would be perfect."
There has been some debate over Pogba's likely position under Mourinho. He said he is capable of playing in a holding midfield role but added: "I feel more comfortable a bit higher."
While he hopes to play in a more advanced position, Mourinho has acknowledged that Pogba cannot match the goal returns of Ballon d'Or rivals Lionel Messi and Cristiano Ronaldo.
Even so, the midfielder is determined to one day be named the world's best player.
"It's true," he said. "That's my dream. That's one of my objectives. I always dream about winning the Ballon d'Or. What's kept me going like this is objectives. I'd rather dream like crazy and say crazy things because it's a dream. I want to dream big things. Maybe it will happen and maybe not, but I will dream it."
Pogba also said he has "big respect" for former United boss Ferguson, despite the controversial nature of his departure, and said he is "the greatest manager in football."
He continued: "I don't have any problems with him and I never had. The only problem maybe I had was I wanted to play. For him maybe it was too early, for me it was too late, and that's it. I respect him, I will always respect him, and I hope to see him again.