The 18-year-old's complicated background means he is eligible for Belgium, Albania and Turkey, while he would also be available for England once he has fulfilled FIFA's eligibility requirements.
As the country of his birth, Belgium would appear to be an obvious choice, particularly as they are on the brink of automatic World Cup qualification.
However, speaking ahead of his side's games against Croatia and Wales, Wilmots confirmed Januzaj does not want to choose at present.
"Manchester United told me that Januzaj has not made a decision to play for a national team yet, not for any country," Wilmots told reporters.
"We gave a clear signal [that we want him to play for Belgium] and now it's up to him. I will respect his choice."
It is thought Januzaj wants to establish a senior club career for himself before making a final decision.
Far stronger than it appears from his slender frame, Januzaj is capable of operating in any advanced position immediately behind a central striker, with the feeling he could develop into a top-class 'number 10'.
He has made a good start, scoring twice on his first United Premier League start at Sunderland on Saturday.
That matchwinning contribution alone should focus minds at Old Trafford about Januzaj's contract, which expires in the summer.
Talks about an extension have been ongoing since April, although so far there has been no resolution.
Little wonder many United fans are fearful of losing the young midfielder as they did with Paul Pogba, who has made such a big impression at Juventus.
Moyes will want to avoid that scenario at all costs given Januzaj is now set to become one of Europe's hottest properties.
Not that the increased scrutiny is going to be a problem according to Phil Jones.
"He is a level-headed guy," said the England international.
"He knows what he has to do. He has to keep his head down.
"He is going to hit the heights though because that was some debut.
"The second goal was particularly impressive. If Gareth Bale gets one of those everyone is raving about it."
Meanwhile, it has also been confirmed Marouane Fellaini will link up with the Belgium squad on Tuesday morning despite being sent for scans on the wrist injury that forced him to miss the Sunderland triumph.
In wishing the former Everton man a speedy recovery, United said on their Facebook site the injury "could keep the striker out for at least a few weeks".
However, the Belgian Football Association has confirmed Fellaini will link up as intended.
Wilmots has not decided whether to use Fellaini, and neither is it entirely clear whether Moyes will wish to persevere with the former Everton man when he returns or send him for an operation it is suggested he needs.
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