The Frenchman has long been thought of as one of the finest players in La Liga outside of the Real Madrid/Barcelona duopoly, and was a key member of his current side’s shock Champions League qualification-winning campaign last season.
Arsene Wenger is believed to be looking at adding top class reinforcements to his squad next month, and is said to be tempted by the skilful 22-year-old.
Reports suggest that the Gunners are set to up their scouting of Griezmann over the coming weeks ahead of a potential move in January.
Although he is a key member of Real Sociedad’s first-team, a source close to the club told Spanish newspaper MARCA that he could be sold for the right price.
“We want to keep him for as long as possible,” he said.
“But we have a battle to convince him to stay – we know clubs are interested in him.”
It is thought that the value in question is around £20m, which fits into Wenger’s current budget – which is estimated to be around £40m-£50m.
A central striker is also a priority, with Liverpool’s Luis Suarez and Karim Benzema remaining the Londoners’ top targets.