A much-coveted asset, the 23-year-old remains relaxed about his immediate future, according to El Mundo Deportivo (via talkSPORT):
I do not think too much about that. I think about playing at the moment and nothing more.
I did not say I wanted to leave this club. This is not the time to talk about this stuff.
Clearly the youngster will have his pick of football clubs should he decide that his future lies away from San Sebastian.
Given Griezmann's skill set and what he brings to the party, Gunners manager Arsene Wenger should aim to pull out all the stops to land the French international.
From a goalscoring perspective, Griezmann's 15 in 26 La Liga games (two as sub), per WhoScored.com, is a more than adequate return from the wide positions.
It compares favourably to Theo Walcott's five in 13 (four as sub), per WhoScored, for example.
Although most view the Frenchman's natural position as out on the left, we have seen him employed in the central and wide-right areas with equal success.
Sociedad's front three enjoy working as a fluid, constantly rotating trio. It gives the Frenchman licence to drift, to drop off where necessary and to utilise his superior first touch and technical ability.
He is particularly dangerous if not tracked and more than once this season he has dragged full-backs out of position to create confusion amongst the opposition defence.
This has invariably resulted in goalscoring opportunities for his team mates, with ex-Arsenal man Carlos Vela a regular recipient. Indeed, the Frenchman's partnership with the Mexican continues to be the key to much of Sociedad's success.
His electric pace and intelligent and direct running has been a nightmare for La Liga defenders throughout this season.
Opposition teams have often made the mistake of sitting back and inviting pressure but given half the chance, Griezmann will shoot on sight.
Indeed, he hasn't been frightened to have a go this season, with 3.2 shots per game, per WhoScored, compared to 2.5 for Walcott.
And unlike a lot of wide players, Griezmann is more than happy to come inside and open up the channels, rather than aiming for the byline himself.
Whilst Arsenal certainly have great creativity in the midfield areas and when Walcott is fit some width and speed, in Griezmann, the Gunners would have the full package.
It's arguable, therefore, that he would be the perfect signing for the Gunners because of the huge variety he has to his game.
Fan Anthony El Tigre is in no doubt who he'd like to see at the Emirates:
If any more convincing were necessary, Griezmann provides it in the shape of his defensive excellence.
He works incredibly hard for the team and his appreciation and understanding of that side of the game marks him out as a truly world class talent.
For Arsenal to move forward and make the leap to genuine Premier League contenders, the acquisition of Antoine Griezmann is a must.