The young Frenchman has been linked with a move to the Premier League for the past few months, with Spurs and Arsenal thought to be competing for his signature.
But Barcelona have now joined the race for the Real Sociedad star. The La Liga giants are reportedly considering a bid should they sell Alexis Sanchez in the summer.
Reports in Spain claim that Griezmann has been identified as the ideal replacement for the Chilean international.
Sanchez signed for Barca from Udinese in 2011, but he's found his first-team opportunities at the Nou Camp limited by the fierce competition for places.
Griezmann first emerged on Arsenal's radar as far back as 2010, when Real Sociedad won promotion from the Spanish second division.
Arsene Wenger sent scouts to keep tabs on the French under-21 international, who came through the academy in Spain.
Tottenham boss Andre Villas-Boas is another fan of Griezmann, but the Frenchman's huge £25m release clause could prove to be a stumbling block.
The report claims Real Sociedad face a battle to hold on to their star player heading into next season, but the club are currently sat fourth in the La Liga table, and pushing for European football.
Griezmann has seven goals and three assists for his Spanish club so far this season, and four man of the match awards.