“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 Barça boss Ernesto Valverde's reign with PSG reportedly willing to pay Neymar's €222 million ($260 million) buyout clause.
Such a fee would smash the current record £89.3 million ($111 million, €105.2 million) Manchester United paid for Paul Pogba last year.
Neymar arrived back in Barcelona on Tuesday from a fleeting promotional tour to China after playing in all three of Barça's glamour pre-season fixtures in the United States against Juventus, Manchester United and Real Madrid.
He arrived for training at 9am local time (0700GMT), but left 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.
Clubs can be sanctioned by UEFA for making a loss of more than €30 million over a three-year period.
PSG have already been fined and saw their Champions League squad limited by UEFA for breaches of FFP in 2014.