Moyes has had plenty of experience in developing young talent. It was the Scot who gave both Wayne Rooney and Ross Barkley their debuts at Everton.
And now he must guide Januzaj through the early stages of his career following the 18-year-old's two-goal matchwinning contribution on his first Premier League start at Sunderland a fortnight ago.
Yet the early signs are positive.
Immediately after that victory at the Stadium of Light, Januzaj's international credentials became the subject of a Europe-wide debate given he could play for either Belgium, Albania or Turkey due to his complicated family tree.
In addition, should he complete five years' residency from the age of 18 in 2018, he could also be able to play for England.
That potential scenario was thrust into the spotlight when Arsenal's England midfielder Jack Wilshere expressed his opposition.
Happily for Moyes, being the centre of attention does not appear to have troubled Januzaj in the slightest.
"He is probably the most level-headed young boy I have ever come across," said Moyes.
"I have had Wayne and Ross and all the other ones who have come through at different clubs.
"He is the most steady and stable."
It appears Januzaj's career will be guided by his father, Abedin, who was Albanian-born but raised in Kosovo.
"The boy is in really good order," said Moyes.
"He is certainly kept in check by his father and his family but mentally he is really good.
"At the moment I don't see any problems.
"Maybe in years to come you will come back and say, 'Do you remember this interview?'.
"But hopefully he goes on to fulfil everything we think he will do."
However, that might not guarantee Januzaj keeps his place for tomorrow's Old Trafford encounter with Southampton as Moyes acknowledges he has the options to rotate his troops.
"I don't think anybody plays every week for Manchester United," Moyes said.
"We have enough players to rotate the squad.
"Adnan is 18, does anyone expect him to play every week? Is he good enough? The answer is yes."