Griezmann announced he would be leaving Atletico Madrid in May before the season had finished and it was expected that Barcelona would sign him.
The Frenchman’s buyout clause is set to drop to around €120million (£106m) - a fee that the Catalan club were going to pay on July 1.
But Sport are reporting that PSG now look likely to land the forward’s signature first, and that Barca won’t put up a fight for it.
It’s thought that the Nou Camp dressing room aren’t keen on welcoming Griezmann with, who has been long-tipped to leave Atletico, open arms.
Sport also say the Griezmann has held a meeting with with PSG chief Nasser Al-Khelafi and that a deal has been signed off on.
Atletico Madrid president Enrique Cerezo said on the situation: "Griezmann has been with us for five years and done a splendid job. We have a good relationship. Nice, trustworthy.
"I hope wherever he goes he will be treated the same as he has been with us.