Moyes helped to put Rooney on the path to superstardom during his days at Everton, with a precociously-gifted teenage talent unleased on the world after learning his trade in the Goodison Park academy ranks.
The pair have been reunited at Old Trafford, but it is Januzaj who is now causing a stir after bursting onto the senior stage.
Still only 18 years of age, the tricky winger has fast become an important cog in the United machine - with great expectations being placed on his young shoulders.
Moyes believes Januzaj has the ability to follow in Rooney's footsteps and become a global star, but insists he will continue to favour a cautious approach when it comes to his ogoing development.
The Scot said after seeing Januzaj put in another eye-catching display against Swansea City on Saturday: "Adnan is in Wayne's category. He's in that territory, definitely, because of his ability.
"But he's slightly different. He's a really calm boy, he looks after himself in a great way. His father has really helped him a lot and because of that he's steeped in football. He works and he lives for it.
"He practices every day and has that little bit of arrogance all top players have in their own way. They want to do something special. They want to take a player on. They want to try something.
"I'd known a bit about him, he had been mentioned to me, but I didn't know enough about him.
"But the minute we got him away with us in pre-season we knew right away there was something there. He can play off the left, he can play off the right. He's a No. 10 and he's played centre-forward. He's that talented a player.
"We want to try and get him on the ball. But we don't want to play him too much because of his age."