Brazil's ARA reports Neymar has had a deal settled with Real for over a month. Terms were agreed during Real's Champions League clash with PSG earlier this season.
Real must now convince PSG president Nasser Al-Khelaifi to sell his star Brazilian, having declared just this week that he was sure Neymar would stay "2,000%".
However, French media sources say Al-Khelaifi also has an idea of what he would accept to sell the attacker - €370m. This would represent a €150m profit on the fee PSG paid Barcelona for Neymar in August.
For his part, Real president Florentino Perez is willing to pay what it takes to clinch Neymar's signing this summer.