The Belgium-born 18-year-old marked his full debut for the Old Trafford-based club with a decisive double as United came from behind to beat Sunderland 2-1 at the Stadium of Light.
When asked if Januzaj could one day play for England, Hodgson, who was appearing on BBC1's Match of the Day as a pundit, 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."
Earlier, United boss David Moyes confirmed in his post-match press conference that the Football Association had been in touch with the Old Trafford club about Januzaj's eligibility.
Asked if the FA had been in touch with the club over Januzaj, Moyes replied: "Yes, they have.''
Januzaj, who is of Kosovan descent, is eligible to play for several different countries already, Belgium, Albania and Turkey among them.
"I think there is some way that he could qualify for England, yes," Moyes added.
"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."