The France striker has been on Barca's radar for a number of months, and parent club Atletico Madrid made a formal complaint to FIFA last year over an alleged illegal approach.
Asked if there had been any contact with Griezmann, Barca president Josep Maria Bartomeu is quoted by The Sun as saying: "I haven't spoken to him this year, but with his agent in October."
According to FIFA's regulations on the status and transfer of players, "a professional shall only be free to conclude a contract with another club if his contract with his present club has expired or is due to expire within six months. Any breach of this provision shall be subject to appropriate sanctions."
Various reports in Spain suggest that Griezmann - under contract at Atletico until 2022 - could be banned from playing for up to six months, while Barca could face the prospect of being unable to sign players in any of the next three to five transfer windows.
Griezmann came close to leaving Atletico last summer, with Manchester United thought to be interested, but performed a U-turn after the club were hit with a transfer ban of their own.