The Belgium-born youngster could become eligible to play for England in 2018 under FIFA residency rules, but Wilshere believes that England should reject the idea and focus on its own pool of players.
He told The Telegraph: "If you live in England for five years, it doesn't make you English. 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. You shouldn't play. It doesn't mean you can play for a country. If I went to Spain and lived there for five years, I'm not going to play for Spain.
"We have to remember what we are. We are English. We tackle hard, are tough on the pitch and are hard to beat. When you think of England, you think they are brave and they tackle hard. We have to remember that."
Januzaj has yet to declare his allegiance for any of the nations he can represent, which includes Belgium, Albania, Croatia and Turkey.