The Ligue 1 champions have been linked with a stunning £40m offer for the 19-year-old ace after being impressed by his fledgling Old Trafford displays.
Januzaj has been one of the few shining lights at United this term, and has responded well to his increased first-team role under David Moyes.
PSG were confident that a big fee and a £100,000-per-week salary would be enough to snap up the Belgium-born winger, but it appears that the Red Devils are closed off to the possibility of selling their teenage ace.
“Adnan has a massive role to play in the future of the team and he can go on to become a huge success at United,” a source close to the club said.
“It doesn’t matter what offers might come in for him, he will not be sold because he is not for sale.”
Januzaj only penned a new contract at United earlier this season, and he could be in line for another one over the summer if he continues to progress at his current level.