The 19-year-old has stated his desire to win silverware with the champions en route to becoming recognised as the Red Devils' finest player.
Januzaj is quoted as saying in The Mirror: "I'm quite pleased with my year. I've done a lot of work and have been integrating into the first team.
"I've played games and I think there's more to come. I hope to win trophies at this club and be the best player."
A recent report claimed that Paris Saint-Germain were weighing up a £40m bid for Januzaj.