The Belgium-born 18-year-old marked his full debut for the club with a decisive double as United came from behind to beat Sunderland 2-1 at the Stadium of Light.
David Moyes: "The FA had been in touch with the club over Januzaj, and maybe Scotland as well. I think there is some way that he could qualify for England, yes.
"I think he's got a choice of countries to play for. He's got probably three or four different countries he could choose to play for.
"Obviously, he has been called up by Belgium several times and chosen not to at the moment, and he's wanted by, I think, Albania, Croatia and a few others as well.
"He can play for several countries - and England as well. I don't know how that is. I think it's something to do with his residency. That's something to do with it.
"He's a very, very good player. But we will do everything we possibly can to keep his feet on the ground. We played him in the reserves at Bolton last Monday.
"That's what we will do at the club. He's a very humble boy, works hard, so we will do everything we possibly can to keep a level on it, but we know we have got a really exciting talent there.
"All young boys want to play for Manchester United. I don't know a better place for them to have the work, the coaching, a club that promotes young players - and I'd like to say a manager who promotes young players as well.
"If I was a dad of a young boy who was good enough, I would be saying, 'I think there's a chance of you getting in the Manchester United team because they push you forward and they promote their young players'.
"That's part of my remit and I was more than happy to play Adnan today."