Griezmann made the big-money switch to the Camp Nou before the start of the 2019/2020 season, but the Frenchman struggled to make an impact.
The 2018 World Cup winner only managed to bag nine goals in 35 LaLiga appearances this campaign, as the Catalan giants finished five points behind champions Real Madrid.
According to Marca, Barcelona president proposed a swap deal that would Griezmann returning to the Spanish capital in exchange for Joao Felix.
It is being reported by the Spanish publication that Bartomeu made the offer just days before the Catalan giants' 8-2 defeat to Bayern Munich in the UEFA Champions League.
However, it believed that Atletico CEO Miguel Angel Gil Marin rejected the offer straight away as they have no intensions getting rid of Felix.