Herrera is out of contract at Old Trafford this summer, when he can leave the club on a free transfer, and has already received a £150,000-a-week contract offer from PSG.
Unai Emery is in need of a new midfielder with Aaron Ramsey joining Juventus in the summer and is a fan of his compatriot.
Foreign clubs are already able to hold pre-contract talks with Herrera, though Arsenal will have to wait until he has been released before making official contact – giving PSG the edge.
Herrera is believed to be looking to almost double his current £80,000-a-week salary, with PSG prepared to offer him a three-year deal, though he would be open to staying in the Premier League.
Speaking about the speculation, Herrera told El Periodico: I do not concern myself with what will happen in four months, so I do not know if my time here is over.