France Football says PSG are keen to bring the former Barca junior back to Europe next year.
Kubo, 16, has been likened to Barca star Lionel Messi and is already a first teamer for his J-League club. He was forced to leave Barca's academy last year as part of FIFA's investigation into their youth recruiting practices.
Barca do plan to bring Kubo back to Europe when he turns 18, however there is now competition from PSG.
France Football says contact has been made with the midfielder's representatives about choosing Paris over Barcelona as his next destination.