Januzaj has enjoyed a breakthrough season at Old Trafford, seeing plenty of first-team action and emerging with an enhanced reputation during a difficult time for the club.
The 18-year-old's form has drawn admiring glances from some of Europe's biggest clubs despite having committed his future to United by signing a new five-year contract in October.
However, PSG remain interested in the teenage winger and have had a January bid turned down by the reigning Premier League champions, according to The Guardian.
The Ligue 1 leaders are said to be looking to tempt Januzaj with the opportunity of Champions League football next season, something that looks unlikely for United as they currently sit six points behind the top four.
However, the youngster rejected offers from France, Spain and Italy earlier in the season and United are believed to be unwilling to negotiate a move for him.