The Catalan giants struggled to find a replacement for Neymar following the Brazilian's world-record £200m switch to Paris Saint-Germain.
Liverpool playmaker Philippe Coutinho was a top target, but the Merseyside outfit refused to sell, even after the 25-year-old submitted a transfer request.
Griezmann was heavily linked with a move to Manchester United, but after Atletico's transfer embargo was imposed, the France international opted to stay loyal to his club of three years.
According to Mundo Deportivo, Barcelona attempted to prise the forward away from the Vicente Calderon with a £124m offer, but both the player and the club turned down a move.
Griezmann has scored one goal in two La Liga outings this season.