The 26-year-old France worldwide signed a new contract earlier this year, committing him to Atletico until the end of the 2021-22 season.
Barcelona-based sports daily Mundo Deportivo reported on Sunday that Barca's president Josep Maria Bartomeu had recently met with Griezmann's family.
Atleti were hit with a transfer ban and the in-demand striker instead committed to a new long-term deal, but Barca have since emerged as strong contenders to sign him.
The Uruguayan global could be allowed to leave if the Catalan club lands its top target; Atletico Madrid's French star Antoine Griezmann and Spurs are said to be potential suitors for the player if the report is to be believed.
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"We can confirm that we have received a complaint from Atletico de Madrid".
Sky Sports says that a Federation Internationale de Football Association spokesman has confirmed to them that they "have received a complaint from Atletico Madrid".
Further reports suggest Robert Fernandez, Barcelona's technical director, spoke to with Griezmann's agent with Guillermo Amor, head of the club's youth development telling Movistar+ that "In the case of Griezmann, there are a lot of players we could be talking with, initiating some kind of relationship if there's an opportunity".
According to Atletico, this violation is made worse by the position of the two clubs, as they are second in the table, six points back of Barcelona, and could have impact on the title race.
"Everyone knows that we defend Atletico, it is a matter of respect".