The most recent articles say the Brazilian wants to move to Spanish giants Real Madrid, who originally tried to sign him in 2013 before he opted to join Barcelona from Santos.
Spanish newspaper Marca reported on Friday that the player's father and agent, Neymar Sr, had told PSG his son wanted to leave immediately.
It said his father met Real directors in December on the day Cristiano Ronaldo received the Ballon d'Or in Paris.
Neymar has been out of action since spraining his ankle and fracturing his fifth metatarsal on February 25, which led him to undergo surgery in Brazil as he bids to regain fitness in time for the June-July World Cup in Russia.