The Red Devils have failed to add to their 20 English league titles since the Scot bowed out as a champion in 2013.
Ferguson recently told Press Box PR that he felt United are "now in the same situation" as Liverpool were when they went 30 years without winning the title.
The club great said it "could be 10 years, 11 years" until the Premier League trophy returns to Old Trafford, but Amorim is confident it will not take that long.
"He understands football more than me, especially English football," the current United boss said. "I think we are not [going to] take that long to win a league.
"I don't know which manager is going to be here, but I truly believe that we can fight for the title in the next [few] years.
"I think it's not going to take so many years, but you never know."
United are sixth heading into this weekend's trip to high-flying Aston Villa, where Amorim will be without six first-team players.
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Injuries to Harry Maguire and Matthijs de Ligt are compounded by Casemiro's one-match ban, while Amad Diallo, Bryan Mbeumo and Noussair Mazraoui are at the Africa Cup of Nations.
Bruno Fernandes is sure to be among the starters at the end of a week that saw an interview with the captain released in which he claimed that "the club wanted me to go" when Al-Hilal made a big-money summer bid.
"The difference is that he spoke with the club before that interview and he said what is his feeling," Amorim said.
"Of course, we can avoid these things because we already know the noise, but he talked with the board and I think everything is clear."
Fernandes also suggested not everybody defended United the way he does.
Amorim said: "I don't know if it's fair. He just spoke about what his feelings are and he has to answer to that. It's not me.
"I think he is an example that he gives everything. He puts everything on the line in every training, in every match.
"In that department he's special, so I think he has that feeling we need to step up and to have also that feeling, so we need to ask him, because I think he's a big example in the group."
