The 66-year-old was asked about the teenager, who scored a brace in the Red Devils' 2-1 win over Sunderland, during his appearance on Match of the Day last night.
Earlier on, United manager David Moyes had revealed that the FA have been in touch over his eligibility as he is yet to decide who he will play for at international level.
"I think he's got a choice of countries to play for," the Scot told reporters. "Obviously, he has been called up by Belgium several times and chosen not to at the moment.
"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."
Later, when asked if the 18-year-old could one day wear the Three Lions, Hodgson said: "Yeah, down the line if he becomes naturalised or if he becomes a homegrown product.
"He's been with United for a long period of time and of course that discussion will have to be seriously debated before we start naturalising players.
"There's no doubt that he's a real talent and we have our eyes on him but a lot will have to be discussed."
Januzaj, who can also play for Albania, Croatia and Turkey as well as Belgium, the country of his birth, joined United from Anderlecht two years ago.