The Catalan giants are desperately looking to reduce their wage bill by offloading players as they need to register Lionel Messi and their new signings.
The club have already offloaded six players in recent weeks, but more are expected to follow with Griezmann reportedly high on that list due his big wages.
Griezmann has been linked with Manchester City and Atletico Madrid, but Calcio Mercato have reported that the Frenchman is keen on a move to Serie A giants Juventus.
It is believed Juventus have already made contact with the Catalan outfit for Griezmann's services and club president Joan Laporta revealed there is a market for the player.
"It's a special market and you have to use your imagination, perhaps thinking in swap deals, but we value Antoine a lot. The club made a big investment in him and we are happy with him," he told reporters, as per Goal.
"It's not easy for a club to come in with an offer for a player at his level. But the transfer window is just getting started and there's a market for Griezmann."