The Brazilian moved to PSG last summer in a world record £198million transfer.
But there have been constant reports in Spain suggesting he is not happy with life in the French capital.
That has led to speculation Real could make a move with Florentino Perez adding to those rumours last month when he said Neymar would have a better chance at winning the Ballon d’Or at the Bernabeu.
However, PSG have told Real once and for all it is impossible the 25-year-old will leave in the summer.
That’s according to the Telegraph, who claim Real could now turn their attention to Chelsea star Hazard.
Real president Perez is expected to splash the cash this summer in a bid to bolster his squad with big-money moves touted for Harry Kane and Mauro Icardi among others.
Hazard has also been consistently linked with a move to the reigning La Liga champions.
His father added to those rumours recently when he suggested Hazard was refusing Chelsea’s offer of a new contract in the hope Real will bid for him in the summer.
But the Belgium international spoke about his father’s comments this week, stating he talked with him about what he said.
And he hinted he is willing to sign an extension at Stamford Bridge.
“I’m focused with Chelsea. I’ve got two years contract left and I’m happy here. Like I said 10 times before, I want to finish this year and then we’ll see. But I’m happy here.”