"The player came to train as scheduled and announced to his teammates that he is leaving," said the source.
"The coach has given him permission to not train and to manage resolving his future."
Speculation over the 25-year-old's future has dominated the first few weeks of new Barca boss Ernesto Valverde's reign with PSG reportedly willing to pay Neymar's 222 million euro (USD 260 million) buyout clause.
Such a fee would smash the current record ?89.3 million (USD 111 million, 105.2 million euros) Manchester United paid for Paul Pogba last year.
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He turned up for training at 9am local time (0700GMT) today, but left less than an hour later.
Presuming both clubs don't come to a late agreement, the buyout clause would have to be paid to Barcelona via Spain's La Liga to free the player from the contract he signed last year and runs until 2021.
However, La Liga president Javier Tebas has threatened not to accept PSG's money over what he perceives as a failure on the French side's part to comply with UEFA's financial fair play rules (FFP).
"We will not accept this money from a club like PSG," Tebas told Madrid sports daily AS on Wednesday.
"Especially when this club is infringing rules and laws."
Barcelona have also threatened to report PSG to UEFA over any potential breach of FFP.
PSG have already been fined and saw their Champions League squad limited by UEFA for breaches of FFP in 2014.
- Champions League dream -
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Winning the Champions League for a first time is the dream driving PSG's owners Oryx Qatar Sports Investments (QSI) to fund a deal that could herald the start of a new era at the elite level of European football.
Prising Neymar from the grip of Barca would truly announce PSG's presence as a contender for the likes of Barca, Real Madrid and Bayern Munich to fear.
Neymar has formed one of the deadliest strike partnerships in football history with five-time World Player of the Year Lionel Messi and Luis Suarez over the past three seasons.
Yet, one justification for Neymar to jump ship on top of the reported offer to triple his salary to 30 million euros net a season, is a desire to move out of Messi's shadow if he is to end the Argentine and Cristiano Ronaldo's decade-long dominance to win the Ballon d'Or.
Neymar's four-year spell in Spain has also been overshadowed by the murky transfer deal which brought him to Barcelona from Santos in 2013.
DIS owned 40 percent of the players' rights at the time of the deal and believe they were deliberately cheated out of their real share due to the complex structure of the transfer.
Disclaimer: No Business Standard Journalist was involved in creation of this content