According to the 'Sunday Express', there are still some minor details to figure out, but the deal could be announced after the upcoming international break.
Real Madrid have been constantly linked with a move for the Belgium international, but their hopes of tempting him to the Bernabeu could now be over.
Hazard's current Chelsea contract, in which he picks up £220,000 a week, expires in 2020, but the new deal will see him earn more than Manchester United star Paul Pogba.
The French international earns £290,000 a week, but Chelsea are ready to do whatever it takes to keep Hazard at Stamford Bridge.