The 18-year-old has broken into the Red Devils' first team this season, scoring twice in a 2-1 win at Sunderland in his first start, being rewarded with a five-year contract and making his Champions League debut against Shakhtar Donetsk on Tuesday.
And he has set his sights on a long-term stint at the club, telling MUTV: "My first opinion was to sign for Manchester United. It was my first choice and I have signed for them.
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"The boss [David Moyes] gave me a chance and I couldn't have asked for more than to score two goals on my debut.
"I was really happy with those goals. Now I have to continue and score more if I can because I have to prove I can play at first-team level.
"Winning trophies is the only thing I want and to try to be the best player."
Januzaj has primarily been used out wide by Moyes but believes that his best position "will be behind the striker as a No.10".
"I always used to play there when I was really young," he explained. "I can also play on the wings and I always do my best. I would do that even if it was at left-back. It is my job. But number 10 is the position I always wanted to play."