The 20-year-old has fallen out of favour under Louis van Gaal this season, and the Daily Star reports that he could be set for a move to Goodison Park in the summer.
The youngster had an impressive season last time out, but has failed to continue his progression and recreate the early signs of promise he showed under David Moyes.
Everton were among the clubs linked with a move for the United academy graduate in January, but the Old Trafford club were reluctant to do business mid-season.
The winger has just eight starts in all competitions to his name this season and has lost his place in the Belgium squad as a result.
Januzaj is also yet to register a goal or assist this season, in stark contrast to last campaign where he netted four goals and bagged three assists in 27 Premier League appearances.