President Josep Maria Bartomeu has taken charge of talks regarding bringing Neymar back to Camp Nou and the idea is that Coutinho will move in the other direction.
Moreover, United are also keen to secure a marquee signing like Griezmann in a transfer window that may see both Paul Pogba and Romelu Lukaku depart.
However, Sport are reporting that French club Paris Saint-Germain are leading the race for the Brazilian and that Coutinho has already "said yes" to the move.
But PSG responded by activating Neymar's clause. Media reports have painted the club as ready to strike a deal if the complicated details will allow it, but Camp Nou vice-president Jordi Cardoner stated last week it is not even being thought about.
Holder wins toss, elects to bat against Afghanistan
Shah and Alikhil refused to throw in the towel, though, frustrating the West Indies attack with a 133-run partnership. Carlos Brathwaite (4-63) dismissed Shah as he and Kemar Roach (3-37) snuffed out Afghan hopes of an unlikely victory.
Javier Tebas has expressed reservations about Neymar returning to La Liga, saying he feels the Brazilian superstar's off-field behaviour could be detrimental to the Spanish league.
Coutinho joined Barca 18 months ago in a club record deal worth a potential €160m.
Neymar spent a trophy-laden four years at Barcelona after signing from Santos in 2013, winning the Champions League and two La Liga titles.
The former Liverpool star is now at the 2019 Copa America in Brazil with his national team. He helped the hosts beat Argentina on Tuesday to reach the final.
There has not yet been direct contact between PSG and Barca.
Coutinho has 21 goals in 75 games for Barca but has never looked comfortable, nor has he cemented himself as a sure-fire starter for Ernesto Valverde.