The French international is widely thought of as one of La Liga’s top talents, and has played a key role in his side’s rise to become one of the division’s better teams over the last few seasons.
It is understood that the Gunners have made the 23-year-old one of their top targets heading into the transfer window, and have had representatives in contact with the Spaniards.
Griezmann has been scouted by the Londoners on multiple occasions over the course of the past few months and is seen as a player that could boost their hopes of domestic and continental success next term.
The youngster is able to play on either flank and has been lauded for his electric pace and eye for goal during his time with Sociedad.
His 16 league goals in 31 outings this term leave Arsenal with competition for Griezmann – Liverpool and Manchester United are also said to be keen – but Arsene Wenger is thought to be confident that an agreement can be reached.
With his contract due to expire in 2016, a bid of £25m is likely to be accepted for the wide-man.