The Spanish giants want to sign Hazard in the summer for Zinedine Zidane.
However, Chelsea playing hard ball over a fee means they may turn to Anderson, per Sky Sports.
The West Ham playmaker would cost roughly £65 million.
While he does not have the same pedigree as Hazard, Real believe he would be a key asset to the team.
Anderson has eight goals and six assists for the Hammers in 31 league games this season.