However, Red Devils legend Nicky Butt doesn't think that success will come overnight, and fans should expect it to take at least two years for the Portuguese boss to build the team he needs.
The Red Devils lost their first game under new manager Amorim on Wednesday, falling to a 2-0 defeat to old foes Arsenal at the Emirates Stadium.
But Butt thinks Amorm is more capable than his predecessor of getting the most out of the current squad, comparing the Portuguese to compatriot and former Man United boss Jose Mourinho.
Joining talkSPORT's White and Jordan show on Thursday, Butt said: "I think what you've got to have at that football club is character.
"If you look at all the managers that come after Sir Alex [Ferguson], whether they've failed or not, they're all people that can carry the club on their shoulders.
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"[Louis] van Gaal, [Jose] Mourinho, they're big personalities, big characters.
"Unfortunately for me I didn't think Ten Hag had that character. I thought he was not good in interviews, he wasn't great on TV, he seemed like he knew what he was doing on a coaching pitch but he didn't transfer [that] onto a game.
"And I think this guy now, Amorim, one thing I think he's got is character.
"Time will tell if he's got what he needs to get Man United back up to the levels [they want] with the investment that's going to have to go into the squad.
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"But he's certainly got it. He's got character, he's got charisma and he looks like he can carry the club on his shoulders - and that's the biggest thing at Man United. I don't care what anybody says.
"Don't forget these coaches, these managers go and get coaches as well so the ones underneath them have to be top coaches as well to coach the players. And he has his own people that he brought in.
"I think it was the right thing to do to get rid of [interim manager Ruud van Nistelrooy] at the time as well because he's [going to bring] his own players in, he's going to have no excuses, he's going to have no one looking over his shoulder, that's not his person.
"He's got his own guys there and if he does it right, I think he'll do well."
Butt's former teammate, Red Devils icon Gary Neville, was furious with his former side's performance against Arsenal - namely the defending for Jurrien Timber and William Saliba's goals from the home side's deadly corners.
And former midfielder Butt thinks it's going to take at least two transfer windows for Man United to rebuild their team to make them capable of challenging for the league title.
"There's going to be a lot of pain," Butt, who made 385 appearances for Man United between 1992 and 2004, continued.
"There's going to be some pain coming, it'll continue to come because he has to go and look at the players and he's got to play them.
"So everyone will be going, 'he's not done anything for the last three seasons, why are you giving him a game?' Because this new guy's got to go in, he's got to give the lads a chance, he's got to see what he's got.
"And then he can go to the board and say, 'I don't want that player, pay his contracts up, pay his contracts up, get that player for me, get that player for me' and he can start building his own.
"And it's going to be two seasons, it's going to be two years.
"It's going to be four transfer windows until we get where we need to be and challenging [at] the top of the table."
Man United sit 11th in the Premier League table after a slow start to the campaign under Ten Hag.
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Amorim has overseen one draw, two wins and one loss in his opening four games in charge in all competitions.
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The Red Devils face sixth placed Nottingham Forest on Saturday at Old Trafford.