The 29-year-old could not prevent his side from being eliminated by Manchester City in the semi-finals of the Champions League, but he has again been in strong form this term despite some injury problems, scoring 15 times and registering 10 assists in 27 appearances in all competitions.
Neymar's existing deal in Paris is due to expire next summer, and Barcelona have again been linked with the Brazil international in recent weeks.
However, according to L'Equipe, the former Santos youngster has agreed a new contract until June 2026, with an announcement potentially arriving over the weekend.
The report claims that the five-year contract will be worth £26m a season, while the South American will receive a substantial bonus if PSG win the Champions League in the coming years.
Neymar has scored 85 goals and registered 51 assists in 112 appearances for the French champions since arriving from Barcelona in August 2017.