According to Sport (via The Sun's Alec Shilton), Barca are ahead of rival suitors Manchester United and Manchester City in the race to sign the French forward, but Coutinho is still the Blaugrana's preferred target.
That's despite a recent report explaining the Camp Nou giants already have a deal in principle with Atleti to sign Griezmann next summer and have plans to negotiate around his €100 million release clause, per Le 10 Sport (via Sport).
Furthermore, Atleti president Enrique Cerezo has said he is confident the club's star man will not leave, per Europa Press (via Football Espana): "People do not understand Griezmann or the sense of humour he has. He wants to stay here, that is what he is saying and nowhere has he said he wants to leave us, in fact he has said the opposite. He has a contract with Atletico [to 2022]."
The 26-year-old was heavily linked with United last summer, but he then committed himself to Atleti when their transfer ban was upheld, saying it would be a "dirty move" to leave, per the Press Association (via the Guardian).
The Madrid outfit's FIFA ban will be lifted, though, come the January transfer window, resurrecting the possibility of Griezmann leaving the club.
He has not enjoyed the best of starts to the new campaign, netting just twice in nine La Liga appearances, per WhoScored.com.
However, Griezmann has proved over the previous three seasons as Atleti's principal attacking threat that he has the ability to be consistently effective in front of goal against the best sides.
As such, it is little surprise Barca are interested in snapping him up for their attack, which is still recovering from the summer loss of Neymar and is overreliant on Lionel Messi.
It seems Coutinho is still their No. 1 target, though, and Barca are determined to return for him despite having three separate bids rejected by Liverpool in the summer—the biggest of which was worth up to €130 million (£119 million), per the Guardian's Andy Hunter.
United are likely to keep an eye on how Barca's ongoing pursuit of Coutinho pans out, as if the Catalans get their man, the Red Devils will likely then be at the front of the queue for Griezmann.