The La Liga giants are supposedly looking to bring the 19-year-old to the Bernabeu over the summer to bolster their attacking ranks, per Ben Burrows in the Daily Mirror:
His superb performances [for United last season] apparently caught the eye of Los Blancos who see him as the perfect summer recruit.
Such is their admiration for the fleet-footed winger they could offer as much as £33m for him, the paper report.
There is no doubt that he is a star in the making and was indeed one of few positive aspects from the Red Devils' woeful Premier League campaign in the 2013-14 season, which saw them finish seventh and cost David Moyes his job.
He scored four goals and claimed three assists in the English top flight last season, per WhoScored.com, and added an attacking verve that United so often lacked.
He is currently in Brazil at the World Cup as part of a much lauded Belgian squad and has received praise from his international teammate and Chelsea striker Romelu Lukaku, per Tim Gray in the Daily Star:
It's great to have Januzaj in the squad with us now. It is like we are already thinking and looking towards the next generation.
He has been brilliant at Manchester United and already in training with us in Brazil he has already been showing his qualities.
However, despite his great potential, he would be a risky signing for Real, especially at the price that is being reported, and at such a young age a move would also be a risk for his own career.
It is difficult to see where and when he would get the game-time at the Bernabeu that is so important for young players to improve on potential.
He is an attacking midfielder who likes to play out wide, but Madrid already have a proven set of players in his position. The likes of Cristiano Ronaldo, Gareth Bale and Angel di Maria would be difficult to unseat in their current positions at the club.
The trio between them scored 50 La Liga goals last season and provided 38 assists, per WhoScored.com. Those kinds of statistics are second to none and illustrate the amount of attacking power Real already possess.
Were Januzaj to make the switch, he would likely be given very little opportunity to make his mark—which could stall his progression. Also, a £33 million price-tag comes with a huge amount of responsibility and pressure which might be too much for the young star.
It is unsurprising that Los Blancos are interested in Januzaj—he looks like a star of the future. But it would be better for the player if he did not make the move to Spain.
Louis van Gaal's arrival could signal good things for the youngster as he will likely be given even greater opportunities as part of the Dutchman's new regime.
Januzaj has already commented on his new boss, per Sky Sports:
"I feel very happy because he is a great manager," he said of Van Gaal. "He’s won a lot and I’m looking forward to working with him. We are going to have a great future."
He is right to think that he has a great future, and it may yet be in Madrid, but he would compromise his progression through lack of playing time and focus if he moved to Spain.
Januzaj can become a huge star, and huge stars—like Ronaldo—often end up at Real, one of the world's biggest clubs.
But the fact that he is already at a massive club in Manchester United and is already part of, and familiar with, the set up at Old Trafford is invaluable.
He is too young to make any big money switch. He should stay at Old Trafford and improve under Van Gaal in a side which can only really get better after last season.