Barcelona president Joan Laporta is set to axe up to 10 stars in a summer clear-out - including Philippe Coutinho and Champions League.
Ronald Koeman's team are set for an overhaul after finishing off the pace in La Liga and crashing out of the Lionel Messi at the last-16 stage.
And it is hoped a squad revamp will help turn around the club's finances after the impact of the pandemic.
One player Barca do not want to lose is Lionel Messi, whose contract expires this summer amid speculation linking him with a move to Manchester City.
Barcelona are confident the Argentine superstar will stay - and that would allow the club to sell Griezmann, according to Sport.
The Spanish publication says the Blaugraunas want to raise crucial funds and drastically reduce their wage bill by selling Griezmann and Coutinho - who has previously been linked with Arsenal.
If Messi stays, Barca will able to press ahead with the sale of Griezmann - while if the No.10 leaves, a higher price tag would be slapped on the former Atletico Madrid striker.
Another player the club want to convince to stay is winger Ousmane Dembele, who has previously been on Manchester United's radar.
Dembele's current contract expires in 2022, and Barca hope to tie him down to an extension. However, the Frenchman will be available for sale this summer if no agreement can be reached.
Miralem Pjanic, Martin Braithwaite, Junior Firpo and Neto could all be sold, as well as centre-back Samuel Umtiti, another player who has previously been linked with Arsenal.
Matheus Fernandes is another player who could be sold, while academy graduate Riqui Puig may be allowed to leave on loan.
Even Gerard Pique, Jordi Alba, Sergio Busquets and Sergi Roberto could be available, with Barcelona wanting to keep the club stalwarts - but on reduced terms.
The club are said to want the four to agree to pay cuts - but are prepared to sell if deals cannot be struck.
Other than Messi, there are just seven players whose positions in the squad are considered to be safe - Frenkie de Jong, Marc-Andre ter Stegen, Ronald Araujo, Oscar Mingueza, Pedri, Ilaix Moriba and Ansu Fati
That leaves Sergino Dest, Francisco Trincao and Clement Lenglet.
Dest is said to be favoured by Koeman - but the right-back's position could change if the head coach is replaced.
Trincao will be safe if Dembele leaves, while Barca are not said to be looking to sell Lenglet, but would consider offers for the centre-back.
Laporta recently told the XXIV Festa de L'Esport Catala: "A cycle has finished, we are entering a process of renewal.
"Starting next week, decisions will be made to build a more competitive team next year in order to win the Champions League and LaLiga.
"When I talk about the end of the cycle and renewal, it is because I think that is what we must do."
