The 19-year-old's previous contract was due to expire this summer, which had resulted in speculation regarding his future with the Premier League club.
PSG, Barcelona and Juventus were heavily linked with a move for the Belgian's services, but he eventually ended the rumours by signing a new deal with United last October.
However, the winger's representative Dirk De Vriese has conceded that PSG in particular were extremely keen to capture Januzaj on a free transfer.
"All the big clubs have tugged at his sleeve. Especially Paris Saint-Germain, who wanted to really go far. Five minutes before we signed the contract extension, an adviser to the president of Qatar made a completely insane offer to us," he told HLN.
"Because Adnan at the end of the season was a free agent, and no transfer fee would be payable, the Qataris were ready for everything, both in terms of salary and signing bonus."
Januzaj has made 34 appearances in all competitions this season, scoring four goals in the process.