The Daily Mail says Januzaj is coming under increasing political pressure in Kosovo to play in the country's first international fixture, against Haiti next month.
Kosovo's first deputy prime minister Behgjet Pacolli has made a plea to the Manchester United winger to commit his international future to the country.
Kosovo are not yet affiliated with FIFA, but they have been authorised to play Haiti in their first official match.
Kosovo general secretary Eroll Salihu said: "The invitation to him (Januzaj) is symbolic but we believe that he is obliged to show his people that he will be there when needed in a historic moment.
"We should have an answer by the end of this week and Januzaj's appearance would simply show that he has not forgotten his people, even (if) he can play only for 10 or 15 minutes."