He also mentioned two injury doubts who could influence his tactical approach, though declined to name them, while defender Harry Maguire and striker Benjamin Sesko remain sidelined.
"We have two doubts for the game but I will not tell you today," Amorim said on Wednesday.
"It will change the way we're going to approach it, let's see if they can play. The rest of the squad is good. Matheus is back. Harry and Sesko are still out."
The return of the dynamic Cunha, who missed two games with a head injury, is a big boost for United, who are in seventh place, three points off the top four.
The 26-year-old Cunha is clearly thrilled to be back, posting a photo of himself on social media in full training gear at Carrington, and writing: "Back back back."
Cunha can reach higher levels
Amorim said United fans had not yet seen the best of the forward, one of the team's key close-season signings.
"He has more levels to go. He's at a different club, different pressure. He was struggling because he was not scoring and because of social media abuse. He was thinking too much about the numbers, but the influence he has in the team is important to us," Amorim said.
"I think he has so much to grow offensively and defensively."
United's French defender Leny Yoro conceded a penalty in their 2-1 victory over Crystal Palace at the weekend and was substituted after 53 minutes.
He looked disconsolate on the bench but Amorim believes the 20-year-old needed to stop beating himself up after mistakes.
"I also spoke with him because he thinks too much, he makes a mistake and then he struggles," Amorim said. "He wants to do everything so well. He's growing, with games and with setbacks, it's not easy for him as a young guy.
"He cannot show that to the people the way he came to the bench, he knows that. It shows he cares, he knows it wasn't his best game. He is fit and ready for the next challenge."
Amorim received some good news with FIFA's announcement that the release period for players heading to this month's Africa Cup of Nations has been reduced from 14 days before a team's first game to seven.
That means Amad Diallo (Ivory Coast) and Bryan Mbeumo (Cameroon), whose countries play on December 24th, should be free for United's home game against Bournemouth on December 15th.