The Brazilian has been part one of the deadliest attacking lineups alongside Lionel Messi and Luis Suarez at Camp Nou in recent seasons.
However, reports in Spain have claimed that one of Neymar's trusted advisors has told him that he should leave Barcelona because he will always be in Messi's shadow.
According to Marca, PSG are willing to meet the 25-year-old's release clause, but only if he decides that he wants to leave the La Liga giants.
The report adds that Neymar will also become one of the highest-paid players in world football as the Ligue 1 outfit would offer him €30m (£26.3m).
The Brazil international has won eight trophies since his move from Santos in 2013.