The Belgian has struggled to find his feet at Real after a series of injury issues since his move from the Blues in 2019.
Hazard is a Chelsea legend, and the fans would welcome him back to Stamford Bridge with open arms.
According to El Nacional, £34 million would be Chelsea's limit to try and sign the 30-year-old Belgian, either in the winter or summer transfer windows.
Whether Hazard is eager to return, given the quality of Chelsea's first team options in attacking positions, is another matter.
Real have also proposed including Blues fullback Reece James in any potential deal for Hazard.
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