The Liverpool playmaker is a reported transfer target for Barca, with reports in Spain suggesting the Catalans have launched 'Operation Coutinho' as they plot a move to sign him at the end of the season.
Neymar said this week he wanted Coutinho to join him at Camp Nou and believes his international team-mate would "totally fit in Barcelona".
And Coutinho returned the compliment ahead of their World Cup qualifier with Paraguay, praising Neymar's ability and influence on the national team.
"Look, Neymar is a great player as we can all see," Coutinho told reporters.
"He is the guy that decides a lot of games, a guy that is fundamental on our national team.
"We have been together over a period of time since the youth teams, and playing beside him, he can change the game easily.
"We give the ball to him and he sorts it out!"
Brazil have won eight matches in a row under new boss Tite, the most recent of those victories coming in the stunning 4-1 victory over Uruguay in Montevideo last time out.
"Of course, it is really cool to see that everyone is with us," added Coutinho.
"Obviously everyone is following Tite's work – he is doing a great job. So this just makes us more confident.
"As you saw in the stadium, there was a lot of positive energy. So it' is really good for us."
Brazil are back in action against Paraguay in Sao Paulo on Tuesday as they look to extend their lead at the top of South American World Cup qualifying.