The discussions were confirmed by Barcelona president Josep Maria Bartomeu on Friday.
Bartomeu held a news conference that was dominated by transfer talk, with the saga of whether Griezmann will be coming to Barcelona seemingly a significant step closer to being resolved.
He said: "There is interest in Griezmann. [On Thursday] our CEO, Oscar Grau, met with Miguel Angel Gil."
Gil is the chief executive at Atletico, who were rocked by France striker Griezmann's announcement in May that he intends to leave the club.
However, paying the reported €120million release clause for Griezmann would appear more straightforward than persuading the French champions to sell their Brazil superstar.
Bartomeu said: "We know that Neymar wants to leave PSG, but we also know that PSG do not want him to go."
According to Marca, Bartomeu said he considered Barcelona's Ousmane Dembele "better than Neymar", and dismissed any suggestion Lionel Messi had asked him to bring Neymar back to the club.
One man who looks like making a Barcelona comeback is the club's former long-serving goalkeeper Victor Valdes, who is primed for a possible coaching role.
Bartomeu said: "I have spoken with Victor Valdes. We would be delighted to have him return home, and in the coming days we will see what position we can offer him."