Hazard has been heavily linked with Real this summer.
Zinedine Zidane is a huge admirer of the Belgium international and he been trying to convince Florentino Perez to launch a raid.
But Barcelona are now also in the market for a new attacker - and Hazard would prefer a move to Real’s arch-rivals.
Neymar, 25, is on the cusp of leaving the Nou Camp for Paris St-Germain.
And with his impeding departure, the Catalans need to source a suitable replacement.
The Brazilian is expected to cost PSG an eye-watering £198m.
And if the transfer is completed, Barca will have plenty of cash to splash.
Despite the speculation, Antonio Conte insists Hazard will not be leaving Stamford Bridge.
He said: "I don't know anything about this situation.
“In the past I read a lot of stories about [Hazard going to] Real Madrid and now there is Barcelona.
"This is the transfer market and we must understand this.
"Will Hazard stay with us? Yes. He is very happy to stay with us and to play for Chelsea."