It is understood he has decided to leave the club after becoming increasingly frustrated at “playing second fiddle” to Lionel Messi.
“Only a miracle will keep him, he really has made up his mind to leave,” says the source.
“At the age of 25, he thinks it’s his time to win the Ballon d’Or,” the source adds. “He believes he can be the best player in the world at another big club.”
It is understood Paris Saint-Germain remain the only current club willing to meet the player’s €222m (£196m) release clause, with Chelsea and Manchester United unwilling to do so.
It is also claimed Neymar is aware that a “growing number” of supporters do not want him to stay, with recent media polls in Globo Esporte and the Barcelona-based Sport newspaper revealing that the majority of those asked think he should leave.
“Barcelona keep asking him to deny stories and to tell publicly what he told them two days ago – that he’s happy at club. But he’s quiet.” said Guillem Balague, Sky Sports’ Spanish football expert, on Twitter.
“Barcelona expect PSG to pay Neymar’s buyout clause this week,” added Balague.
Barcelona president Josep Bartomeu has said Neymar is not for sale.