Gunners boss Arsene Wenger has returned for the 23-year-old French international after failing to seal a move back in January.
The La Liga side insisted he was not available back then but havesince admitted defeat as the winger eyes a move away from the Anoeta Stadium.
Serie A giants Juventus are also thought to be interested in Griezmann and are expected to at least match Arsenal’s bid, but it’s believed the player would prefer a move to the Premier League rather than Italy.
If Wenger manages to finally get his man, he could be join fellow Real Sociedad teammate Carlos Vela, who Arsenal are expected to return for via a buy-back clause after initially offloading the Mexican to Erreala two years ago.
Griezmann is a versatile winger capable of playing on both sides, and as a number 10.