The 18-year-old, also eligible for Belgium, Serbia, Croatia, Kosovo and Turkey, has yet to declare for a country, with the Balkan nation the latest to try and recruit him
Winger Januzaj, who came to international attention with a game-changing double against Sunderland at the beginning of October, is eligible to play for Belgium, Serbia, Croatia, Kosovo, Turkey and Albania, while England are also keen to try and recruit the teenager.
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"We are ready to accept anything just to have the young, talented Januzaj become part of our national team, so he can contribute for the future of the Albanian football," an Albanian FA spokesman said.
"As we did with other players already playing for the national team, we will continue our job with no hesitation or any influence on us, in order to have Adnan Januzaj wear the black and red shirt, so he can honour himself, his family and the flag of his heritage."
Januzaj was born in Belgium but has so far rejected any advances, with the player's father keen for him to represent Albania, while England boss Roy Hodgson has admitted the Three Lions are monitoring the situation.
"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," he said in October. "Yes [he could play for England] down the line if he becomes naturalised or if he becomes a home-grown product."