Sports daily Marca says Real are ready to make a 50million euro offer for the 22-year-old.
Fabregas himself insisted last week that he was happy at Arsenal.
He told The Daily Mail: “I want to continue to be part of what is happening here. Definitely.
“If not I would have left when I had the opportunity, three years ago, two years ago or last year.
“I believe in this team and I feel we can achieve things. The boss believes in us more than anyone, and I feel I am part of it. He makes me see that as well. And I don’t want to fail here.”