Coutinho opens the door for a Neymar, Barca reunion
Neymar left Barca for Paris Saint-Germain in a world-record move last summer but there has been speculation that he could either return to Barcelona or join Real Madrid.
Barcelona have said they are not aware that Neymar wants to return after reports after PSG's elimination from the Champions League claimed he would push for a move from the Ligue 1 leaders.
But speaking at the launch of the Mediterranean Internation Cup, Coutinho said: "Neymar is a great player. I play with him for the national team and it is a real privilege.
"It would be great if he came back to Barcelona, and of course we would open the door to that."
Catalan newspaper Mundo Deportivo reported last week that Neymar wanted to move back to the Camp Nou.
However, Barca spokesman Josep Vives said that was a "hypothetical debate" and Neymar had not approached the club.
"We are not aware of Neymar wanting to return to Barcelona," he told a news conference.