The 18-year-old, whose second-half brace handed the defending champions their third Premier League win of the season at the Stadium of Light, is out of contract at the end of the season.
United are reportedly confident of tying the youngster down to a new five-year deal, and Moyes is expecting Januzaj to stay despite reported interest from local rivals Manchester City.
“I’m not too worried about that [the contract negotiations] because I think every young boy wants to play for Manchester United,” Moyes told Sky Sports.
“If I was a young player I don’t see anywhere else better than Manchester United.”
The Scot went on to praise the Belgian’s display after watching his side move up to ninth place in the Premier League table.
“I remember giving Wayne [Rooney] his debut and people like Ross Barkley – and Adnan’s certainly of that quality. He’s a top, top player,” said Moyes.
“I would have actually played him two or three weeks ago but for different reasons it just didn’t quite work. I thought today was the right time, he’s been so good, it was hard to stop him.
“He’s going to be a special talent. He showed that he’s got goals and ability on the ball.
“But we’ll keep his feet on the ground here. We had him in the reserves last Monday so we won’t let him get ahead of himself. We’ll try and keep doing the right things with him.”
Moyes also credited his side for their overall performance despite falling behind to Craig Gardner’s opener early on.
“I thought it was just a really good performance,” he added. “Even at 1-0 down I think we played really well. We made a real hash of the first goal but apart from that I thought we played some really good stuff today.”
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