Sky Sports News understands that Neymar decided to leave the Catalan club following talks on holiday near Rio de Janeiro in early July, before he joined the club’s pre-season tour of the US.
He is expected to arrive in the French capital by Friday at the latest to complete his move.
Barcelona spokesman Josep Vives confirms Neymar has asked to leave the club.
It is understood the total value of the five-year deal is worth nearly £450m (€500m) – including wages, bonuses and a buyout clause of £198m (€222m).
Neymar has been offered a basic salary of £26.8m a year (€30m) after tax, which comes to about £515,000 a week.
Barcelona confirmed the buyout clause will have to be “deposited in its entirety”.
A source in Spain close to Neymar has told Sky Sports News: “Since he decided to leave, Neymar has had to deal with huge pressure to stay at Barcelona. His teammates wanted him to stay but his decision was made.”
The source went on: “People will say this has been driven by money, but he wants to become the leader at the club. He wants to be independent, and wants to win the Ballon d’Or. He believes he can do that in Paris.”
PSG has yet to confirm whether an agreement has been reached.
Since joining Barcelona in 2013, Neymar has helped keep the club at the pinnacle of European football and turned into a worldwide star.
He has teamed up with Lionel Messi and Luis Suarez to form an almost unstoppable attacking trio.
Neymar has scored more than 100 goals for the club and helped the Catalans win the Champions League, two La Liga titles, three Copa del Reys, one Club World Cup, a UEFA Super Cup and two Spanish Super Cups.
He came third in the 2015 Ballon d’Or vote. The prize has been shared by Messi and Real Madrid’s Cristiano Ronaldo for the past nine years.