This announcement for a €120million (£108million) switch came on July 12, but Atleti claims the deal was done before July 1 – the day on which the attacker’s release clause dropped from €200million to €120million.
They want an extra €80million (£72million) from Barcelona and have contacted LaLiga in an attempt to secure this money.
“It is possible to block a player’s transfer,” LaLiga president Javier Tebas told Onda Cero.
“La Liga will have to decide what course of action to take.
Atletico Madrid are demanding £72million more than they have been paid
“[Atletico] submitted a complaint and put in doubt whether we should pass Griezmann’s license to Barcelona.
“There’s a process that has been put in motion and those overseeing it will have to come to resolve the case.”
On July 23, Griezmann made his debut for Barca in a 2-1 pre-season defeat to Chelsea.
Atletico’s initial statement on the matter read: “Antoine Griezmann, represented by his lawyer, has appeared at the headquarters of the Professional Football League to unilaterally terminate the contract linking the player with Atlético Madrid, with Fútbol Club Barcelona having deposited the sum of €120million euros in the name and on behalf of the footballer.