Spanish publication 'Sport' reports that the Catalan side face a tricky choice as they look to bolster their ranks when the transfer window re-opens.
It is claimed that Liverpool's Brazilian playmaker Coutinho remains the club's top target, though Barca will also keep their irons in the fire regarding Griezmann, should the English side once again rebuff their advances.
Getting a deal for Coutinho over the line has become something of an obsession for the Barca board, who are keen to make one final push to sign the 25-year-old, despite Liverpool's repeated insistence that they have no intention of selling.
If Jurgen Klopp's side maintain that stance come January, Barca will reluctantly start looking for alternative options, wth Griezmann thought to be top of their wishlist. The Atletico Madrid forward is rumoured to have a €100m buy-out clause in his contract at the Wanda Metropolitano, something which seems well within the reach of Ernesto Valverde's side following the sale of Neymar to PSG during the summer.
However, Barca are by no means the only side looking at Griezmann, with fellow European powerhouses Manchester City, Manchester United and PSG also thought to have expressed an interest in the French international.
Whilst it remains to be seen where the two players' futures lie, one thing is for certain, they won't both be heading for the Camp Nou in the New Year.