The French forward tops a Barcelona list including Everton's Richarlison and Arsenal's Alexandre Lacazette, according to ESPN.
The Blaugrana are keen to add to their striking options and see Atletico's Griezmann as the ideal player to complement Luis Suarez and Lionel Messi.
Any business will be done after July 1 when the World Cup winners release clause drops from €200m (£172/$224m).
