Real Madrid could challenge Barcelona for Neymar in one of the biggest transfer battles of the summer, Sky Sports News understands.
Following reports in Spain, it is understood that Real president Florentino Perez is interested in signing Neymar alongside Barcelona, who dream of putting him in new front four with Lionel Messi, Luis Suarez and Antoine Griezmann.
PSG's sporting director Leonardo has already confirmed that Barcelona have contacted them about signing the Brazil star, but he also said: "We have not seen that Barcelona are truly in a position to buy him. A move of this magnitude is not just a question of emotions. It is a financial question."
It is claimed PSG officials have a stronger working relationship with Real Madrid than Barcelona, following Neymar's world-record £200m move to the French capital from Barcelona in 2017.
No formal offers have been made for Neymar at this stage, but one option Barcelona are understood to be suggesting is a deal that includes players going the other way.
The club are understood to want to offload Ousmane Dembele, Philippe Coutinho, Ivan Rakitic and Samuel Umtiti this summer and hope to get substantial fees for them.
In the next immediate stage of their plans, Barcelona are expected to pay the release clause for Atletico Madrid's Griezmann in the next seven days, possibly as early as Friday.
Neymar, meanwhile, failed to return to pre-season training this week and PSG are considering whether to withhold a monthly bonus in his contract as a result.
The Ligue 1 champions are discussing their options and it is believed they are treating his no-show seriously after claiming there was no agreement for him to extend his stay in Brazil after Copa America.
Every player at the club is entitled to receive the bonus, based on fulfilling contractual obligations, which includes conduct.
PSG's version of events is disputed by Neymar following a strongly-worded statement on Monday. He expects to return to PSG on Monday July 15 after injury prevented him from taking part in Copa America for Brazil.
Real Madrid, meanwhile, have already been very active in the transfer market so far this summer, spending nearly £300m on Eden Hazard, Luka Jovic, Eder Militao, Ferland Mendy and Rodrygo. They too want to offload a number of players this summer.