Barcelona were tipped to re-sign the Brazil international before the European transfer deadline next week.
Reports this week claimed Barcelona have agreed a fee with PSG for the forward.
However, according to Spanish outlet Mundo Deportivo, it will take a drastic change for Neymar to end up at the Nou Camp.
They say Barcelona have rejected PSG’s counter offer, adding a deal is ‘practically ruled out’.
PSG demanded £195m (€215m), Ousmane Dembele, Ivan Rakitic and Jean-Clair Todibo.
However, Barcelona studied PSG’s proposal and refused to give in to their demands.
A lot has been made of Neymar’s move to the Nou Camp, Barcelona defender Gerard Pique wants Neymar to snub a move to Real Madrid.
“We know Neymar is a great player, and not only a great player, he is a great team-mate,” Pique told Express Sport while at PokerStars’ European Poker Tour [EPT] in Barcelona.
“I hope he comes here with us to Barcelona but also Real Madrid is another big club.
“It is normal that they are interested in trying to sign him.
“I don’t know man. Let’s see what happens this week.
“Everything is speculation. Let’s see at the end if he arrives here or not.”
Barcelona and Real Madrid are battling to land Neymar before the European transfer deadline.
However, after Barcelona pulled the plug on the deal, Real Madrid may choose to up their interest in the Brazilian.
Reports suggested Neymar is only interested in returning to the Nou Camp.