Januzaj has enjoyed a stellar season with Manchester United but the 19-year-old is yet to pledge his allegiance to one country at international level.
The forward is certainly not short of options. He can play for his country of birth - Belgium, and either Albania, Turkey or Kosovo through his parents.
England are also interested. Januzaj would have to wait until 2018 to play for the Three Lions, although that idea is complicated by the fact that the Home Nations have opted out of FIFA's residency rules.
Hodgson is a fan of Januzaj, but he will leave it up to the FA to decide whether it wants to try to pursue the player.
"All I can say is that it's a matter for the FA Board because it raises a lot of issues," the England manager said.
"Until such time as the FA board have it very clear what their policy is going to be, is it going to be simply following FIFA dictates or slightly different in some way, all I can do is wait and see.
"But the one thing you have to understand with Januzaj whichever way England decide to go, with the way the rules are at the moment, there's no way he can play for England for the next few years."
Januzaj, who speaks little English, is thought to be assessing his options before deciding which national team he wants to pledge his allegiance to.
Arsenal midfielder Jack Wilshere caused controversy last year when he claimed the idea of seeing the likes of Januzaj play for England made him uncomfortable.
Wilshere told a press conference last October: "The only people who should play for England are English people... If you live in England for five years it doesn't make you English."
Wilshere later claimed his quotes were taken out of context.
Last summer Brazil-born striker Diego Costa committed himself to playing for Spain, where he plays with Atletico Madrid.