Sky Sports reports Moyes revealed the winger is steeped in football after another positive display against Swansea at the weekend:
Adnan is in Wayne's category. He's in that territory, definitely, because of his ability.
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.
Moyes first worked with Rooney when he was a 16-year-old coming through the ranks at Goodison Park almost 12 years ago.
And when Belgian-born Januzaj scored his first goals for the club in a 2-1 victory at Sunderland in October, Rooney said he hoped to play with the winger at international level, per Martin Hardy of the Independent.
Januzaj's form has been a shining light in what has so far been a difficult first season for Moyes at Manchester United.
The reigning champions currently sit seventh in the Premier League having already lost six games, and they were recently knocked out of the FA Cup by Swansea in the third round.
But is Januzaj just like Rooney? The Times' James Tucker believes he stepped up when United needed him in the absence of Rooney and last season's top scorer Robin van Persie:
How about his impact in the Premier League this season?
Januzaj, quite obviously given his age, is still to prove he can perform in the big games as Rooney can.
He may get a chance should United get past Sunderland in the second leg of their Capital One Cup semi-final against Sunderland.
Either way, the signs are there for a promising future.