Hazard is being linked with a move to Real Madrid after admitting he is torn between signing a new contract at Chelsea and joining the Spanish side.
Real failed to directly replace Cristiano Ronaldo during the transfer window, leaving the door open for Hazard to join them.
Morata left Real in 2017 after failing to cement a place in the starting XI.
And in an interview with Depotes Cuatro, Morata revealed he and Hazard had talked about Real.
When asked if Hazard would fit in at Real, Morata replied: “You can put him anywhere.”
He then added: “It’s not that he wants to leave Chelsea but if Madrid is going to go for him.
“It’s not an impediment for him.”
Morata then offered some hope for Chelsea saying: “He has a good relationship with Chelsea.
“It is not like other players that want to abandon a club.
“He’s also going to think about Chelsea.”
Speaking after scoring his eighth Chelsea goal of the season, Hazard said he was reluctant to cause drama in an effort to leave.
“I don’t want that,” Hazard said.
“I want what’s good for me, but I want what’s good for the club because the club has given me everything.
“I don’t want to say: ‘Yes, I am signing a new contract’ and then, in the end, I don’t end up signing.
“So I will see. Sometimes in my head, I wake up in the morning and think I want to go.
“Sometimes I think I want to stay. It is a hard decision. It is my future. I am 27 and I will turn 28 in January.”
According to ESPN, the ball is firmly in Hazard’s court with Chelsea willing to meet his wage demands.
Previous reports had suggested finances could be a problem but the Blues are happy to make the 27-year-old their best-paid player if he commits his future.
They state they are willing to sign the deal ‘tomorrow’ if they see any signs of encouragement that he wants to stay.
His team-mate Ross Barkley, meanwhile, has pleaded with Hazard not to follow his dream and quit Chelsea for Real Madrid.
Barkley admitted yesterday he had been inspired by playing alongside players of the calibre of Hazard.
He said: “Eden is a fantastic player. He has his own dreams.
“I’d love him to stay because he’s really important. But it’s in his hands. I can’t speak for him.
“He loves the club, he’s achieved big things and if he stays I’m sure he’ll achieve many more and win more trophies at the club.”