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 - who also believes Januzaj is close to signing a new contract at Old Trafford - 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.
Talks about an extension to his United contract have been ongoing since April with some fearful of losing the young midfielder as they did with Paul Pogba, who has made such a big impression at Juventus.
But teammate Phil Jones - who saw the youngster make a stunning two-goal full debut at Sunderland - believes the teenager will take all the attention in his stride.
"He is a level-headed guy. 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."