Sky Sports has confirmed that Chelsea refused a £ 60 million offer from Real to join Hazard earlier this month.
In the case of continued rejection, the Spanish club may resort to another wing, the Brazilian Anderson.
Hammers joined the team during the last summer transfer from Lazio, and brilliantly impressed with coach Manuel Pellegrini.
The contract with Anderson is expected to be around £ 65 million, which means a significant gain for West Ham, with a combined 33.5 million.
The 25-year-old has participated in 31 appearances for West Ham this season, scoring 8 goals and making 6 more.