The 25-year-old missed five months of last season with thigh and calf injuries, and has been out for two months of the current campaign after suffering hamstring and head injuries.
“United fans, you may not know me too well yet but one thing I can guarantee, I will never give up or lose faith,” Mount said.
“I’ve said this before, but I will continue to give everything, get through this tough period and won’t stop until that’s achieved.”
Amorim, who took charge of United on 1 November, said he will “help” Mount through his injury struggles.
Asked whether Mount is injury prone, Amorim added: “That is not my department.
“What I can do is help Mase to teach him to play our game while he is recovering, to give him that time to think about different things.
“With Mason Mount, we are going to help him and it is really hard for him to be out so long. He is trying really hard. If they try hard, we will help them to the end.”
