The Spanish publication say the sports brand might be willing to help finance his move back to La Liga.
However, it’s suggested they’d want something in return.
Real Madrid currently have a lucrative association with Adidas.
Nike, however, want to muscle in having lost their contract with Manchester United to the German business.
But he hasn’t found life easy in Paris.
The 26-year-old had a high-profile spat with Edinson Cavani and has struggled to enamour himself to the PSG faithful.
“Real Madrid target Neymar could leave PSG this summer”
He’s also now been ruled out for the rest of the season and faces a race against time to be fit for the World Cup.
Ivan Rakitic has openly admitted he wants to see Neymar back in Catalonia.
“He has not called me, but if it was up to me, I [would] open the dressing room door for him again,” he told Spanish newspaper AS.
“I would love to have him in my team, I would always have Neymar in my XI.”
Neymar has scored 29 goals and provided 19 assists in his 30 appearances for PSG this season.
He won eight honours during his time at Barca, including the 2014/15 Champions League and two La Liga titles.