PSG have promised to take "appropriate action" after Neymar failed to report for preseason training "without the club's prior authorisation."
Sporting director Leonardo has admitted there have been "very superficial contacts" from Barcelona, with Les Parisiens willing to sell if they receive the right offer.
In a statement on the team's official website, the Ligue 1 champions expressed regret Neymar wasn't in attendance on Monday: "Paris Saint-Germain notes that Neymar Jr was not in attendance at the agreed time and place."
Neymar's father has told Fox Sports Brasil (h/t ESPN FC's Jonathan Johnson) PSG were aware his son wouldn't be returning Monday. The player had been in attendance to watch Brazil beat Peru 3-1 in the 2019 Copa America final in Rio de Janeiro on Sunday.
However, Leonardo has confirmed Barcelona's interest to Le Parisien (h/t Johnson), and he said the club will listen to offers for the Brazil international:
Leonardo also told Le Parisien (h/t Goal) how Barca president Josep Maria Bartomeu has been in touch: "They said they wanted to buy but we were not sellers. [Bartomeu] is the one saying it, but we did not see that Barcelona was really in a buyer position."
Neymar has reportedly told Barca he is "desperate" to exit the French capital and return to the Camp Nou, according to Sport's Joaquim Piera.
Reuniting with Lionel Messi and Luis Suarez along the Barcelona forward line would likely appeal to Neymar. The trio helped the Catalan club win La Liga, the Copa del Rey and UEFA Champions League in 2015.
Even so, the 27-year-old hasn't been short of success since moving to the Parc des Princes for a world-record transfer fee back in 2017. He's won the Ligue 1 title in both of his seasons with PSG, as well as the Coupe de France and the Coupe de la Ligue.
Yet for all the trophies, Neymar's time in Paris has also had its challenges. Further success has eluded him in the Champions League, with Les Parisiens falling to Real Madrid in 2018 and Manchester United last season.
Injuries have also been an issue, with Neymar missing several months this year due to a broken metatarsal.
Rumours of a return to Spain have lingered throughout Neymar's time in France, and PSG sound like a club growing tired of the brewing saga. Club president Nasser Al-Khelaifi telling France Football (h/t Vaishali Bhardwaj of the London Evening Standard) last month: "Nobody forced him (Neymar) to sign here. Nobody pushed him to. He came with a fully understanding of the cause to sign up to a project."
PSG's promise to punish Neymar for missing the start of preparations for the new campaign can be read as a further attempt to prove the biggest superstar in the team isn't above the club.
Taking a hardline could be Leonardo's way of controlling his countryman:
The more Neymar and PSG seem at odds, the more rumours of a move to Barcelona will grow. Barca are expected to sign Antoine Griezmann from Atletico Madrid for €120 million, although the buying club wants to pay in instalments, per Sport's Toni Frieros.
Signing both Griezmann and Neymar in the same summer would be a tough needle to thread financially, even for a club with Barcelona's spending power. The more Neymar becomes alienated in Paris, the more he may tempt Barca to make a choice between prime summer targets.