Mainoo has made 12 appearances this season, with one League Cup start, and is set to miss United's game against Newcastle United later on Friday due to a calf injury.
Amorim said the 20-year-old will have to be patient, but he will get his chance in the side.
"Kobbie Mainoo will have the opportunity, he has all the time," Amorim told reporters on Thursday.
"He played in different positions, and we talk about the position of Casemiro, he can do that position.
"If you play with three (in midfield), he can play - like we played in the last game - the position of Mason Mount in this game, he can play there.
"So, in the future, he's going to be the future of Manchester United. That is my feeling.
"So you just need to wait for each chance, and everything can change in football in two days."
With United's squad missing several players due to injury and the Africa Cup of Nations, Amorim said it would be difficult to accept any request from a player to leave in January.
"It's going to be hard for someone to leave the club if we don't get a substitution," the Portuguese said.
"We are short. Even with the full squad, we are short for something that can happen."
Manchester United are seventh in the league with 26 points from 17 games.