Hazard, his team-mate Thibaut Courtois and Bayern Munich’s Robert Lewandowski are the top targets for Real Madrid this summer.
The Premier League champions are seeking to avoid a double exit at the end of the season.
Hazard’s current contract runs until 2020. He is valued at over £200million by Chelsea and his new contract will reflect that with a salary expected to be around £300,000 a week plus bonuses.
Hazard has consistently said he is happy at Chelsea though is understood to be waiting to see what Madrid offer.
Real manager, Zinedine Zidane, is a huge admirer of Hazard but his position is under threat this season and that could yet have a bearing on the Chelsea star’s decision.