The 18-year-old's complicated background means he is eligible for Belgium, Albania or Turkey, whilst 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 match-winning contribution alone should focus minds at Old Trafford about Januzaj's contract, which expires in the summer.