The 18-year-old scored twice during his first Premier League start against Sunderland, while Roy Hodgson has revealed the Football Association is monitoring the situation of the Belgium-born midfielder.
Januzaj is also eligible for Croatia, Albania and Serbia but Wilshere has dismissed the idea of the midfielder playing next to him at Wembley.
"No, for me, if you are English, you are English, and you play for England," Wilshere told reporters. "The only people who should play for England are English people.
"If you've lived in England for five years, for me, it doesn't make you English. You shouldn't play. It doesn't mean you can play for that country. If I went to Spain and lived there for five years, I'm not going to play for Spain. For me an English player should play for England really."
Wilshere also believes a national team manager should also be from the same country, before highlighting the impact Fabio Capello had on his international career.
"I think it's better if there is an Englishman [in charge], but don't get me wrong, Fabio Capello did a lot for my England career," he said. "He brought me here, gave me my debut and stuck with me form a young age, so he was a good manager as well."