The 21-year-old, who has been at Old Trafford since 2001, had previously only been utilised in the League Cup.
But after making his Premier League bow in the recent 2-0 victory over Stoke City after first-choice shot-stoppers David de Gea and Anders Lindegaard were both unavailable, Amos has set his sights on more starts.
"I hope I'm No.1 here at United, that's my aim. I hope to be playing week in, week out. I'll be 26 then and I guess I'll be in my prime," he told the club’s official website when asked where he saw himself in five years' time.
"It's what I've always wanted to do. When people started to ask me what I wanted to do as a job, it was to play for United.
"I saw Peter Schmeichel playing and I had my mind set on it from then. I think I've worked too hard not to be patient and obviously you don't want to give up on your dream.
"Whilst I'm not playing regularly, I still believe I can do it. While that belief is there, I will persevere."
After keeping a clean sheet in the victory over the FA Cup runners-up, the England Under-21 international has admitted he was delighted to kickstart his Red Devils' career.
"It was really good," said Amos. "Obviously, I said after the game I'd been waiting a long time to play in the Premier League. I had played first-team games before but this was a big milestone.
"I've been trying to stay patient all season and have been dying to get out on loan at times. Everything happens for a reason though so it was probably a good job I didn't go out on loan."
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