Real management would prefer to focus on Marcos Asensio rather than splash out on Hazard.
Hazard's father claimed he had rejected a new deal at Stamford Bridge as he was waiting to see what could transpire at the Bernabeu.
However, during a recent boarding, Marca quote a senior a senior member as asking: "Why do we need the Belgian when we have Asensio?"
The young Spaniard was the breakthrough star of Real Madrid's stellar campaign last season, but has barely featured this term.
But many at Real believe a move for Hazard could scupper the development of Asensio, and Real Madrid are determined not to let that happen.