Arsaenal, Liverpool and Manchester United are linked with a move for Griezmann who only signed for the La Liga outfit last summer.
The 29-year-old endured an indifferent first campaign at the Nou Camp, although he did manage to find the net on 15 occasions.
Griezmann arrived at Barcelona from Atletico Madrid and cost the Catalans giants £107 million (BBC).
With Lionel Messi now seemingly set to stay at the club, it could force Griezmann down the pecking order again.
It doesn’t appear that the French World Cup-winning player is part of Ronald Koeman’s plans and that could interest Arsenal and Liverpool.
The Gunners have already bolstered their squad this summer with the signings of Willian, Gabriel Magalhaes and the return of Dani Ceballos.
If they were to add anyone else to their ranks this summer they’d probably need to sell first.
It also seems inconceivable that Liverpool will splash the cash to take Griezmann to the Premier League, especially considering their Premier League success last season.
Roberto Firmino is the main focal point of Liverpool’s attack through the middle and it seems unlikely Jurgen Klopp will look to replace him just yet.
With that in mind, it would seem only likely that either club would make concrete offers if they could potentially take Griezmann on loan first.
The diminutive performer is thought to be on £359,000-a-week at Barcelona and right now, any move away from the Nou Camp might be some way off.
Given the style of football that Mikel Arteta is trying to play and the system he operates, it’s difficult to imagine where Griezmann might fit in.