The 18-year-old, whose family left Kosovo for Belgium before he was born, is eligible to represent a number of different countries on the international stage.
Wilmots had hoped Januzaj would be part of his squad for the World Cup qualifiers against Croatia and Wales, but was told the player had not yet made a decision about his international future.
Reports suggest he may be waiting to see if Kosovo will receive official recognition from FIFA.
Quoted by the Daily Mail, Wilmots said: "This was the first time I have tried to include him in a squad, because I wanted to send him a clear message.
"Unfortunately, I had a very quick response from England, when Manchester United called me to say the player felt he was not ready to make a choice about his international future.
"I respect his stance. Every player has the right to make his own choice, and I will not attempt to make any sort of ultimatum to him. But I do intend meeting Adnan and his entourage to find out for myself exactly what their thoughts are. You cannot force a player to choose a country. It has to come from his heart.
"Clearly, when you have a player of his technique and ability, the door to the national team always stays open."
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 this 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.