Januzaj, 22, burst onto the scene at United in the 2013/14 campaign under David Moyes.
But he has failed to live up to his potential with the Belgium international struggling to impress during loan spells at Borussia Dortmund and Sunderland.
It is said Jose Mourinho is keen to offload the winger this summer and wants around £8.8million for him.
Celtic, Real Sociedad and Marseille have been linked with a move for Januzaj.
But Belgian outlet DHNet claim Roma have now entered the race to sign him as they bid to bolster their ranks ahead of next season.
It is said Roma director Monchi is looking to bring him to the Italian capital.
The Serie A side have apparently been monitoring the player very closely and are prepared to offer him the chance to end his Old Trafford nightmare.
DHNet add an agent has even been hired to help set up negotiations between the two clubs and Januzaj.
Manchester United manager Mourinho confirmed in April that he has already made a decision on Januzaj’s future, but he refused to give anything away.
When asked about Januzaj, he said: “Yes. I have decided. Can I say what it is? Not to you!”
Januzaj only has 12 months remaining on his contract at United.
