The Belgian was initially registered for the UEFA Youth League but was added to the senior squad once he became eligible to feature on the club's B list of players.
An unused substitute for Sociedad's group stage visit to Old Trafford a fortnight ago, United manager David Moyes says the 18-year-old could feature at the Anoeta Stadium on Tuesday.
Januzaj is available for United's return match with the Spanish side
"He's definitely ready to play [in the Champions League]," Moyes told the United website. "He's not got a problem. We're trying to bring the boy along at the right pace if we can.
"He's not tired and we've not seen any dips in form just now so I'm sure we'll continue using him and he'll definitely be in and around the squad."
Michael Carrick, Jonny Evans and Rafael were not involved in first-team training on Monday morning.
Carrick missed the weekend's Barclays Premier League win at Fulham with a calf problem while defenders Evans (back) and Rafael (ankle) were substituted at half-time.