After impressing during the club’s pre-season tour, Januzaj has enjoyed an eye-catching start to the 2013/14 campaign, making his Barclays Premier League debut against Crystal Palace earlier this month.
He also appeared off the bench in Community Shield win over Wigan and in Wednesday’s Capital One Cup victory over Liverpool.
The 18-year-old Belgian’s current deal expires at the end of this season but United are keen to tie him down for the long term.
"As far as I know, things are moving along," Moyes told a press conference on Friday. "As soon as we get the news, we will give it to you."