The Blues have been trying to convince the 27-year-old to sign a new deal, but have had no luck so far
Real Madrid are believed to be preparing a £150million bid to bring Eden Hazard to the Bernabeu.
Hazard, who captained Belgium to a World Cup semi-final has two years left on his current deal.
Chelsea have been trying to persuade the 27-year-old to sign improved terms for around a year and are willing to give him the most lucrative contract in their history worth around £300,000 a week.
However, he is aware it could be his last big one and explained he is therefore considering a number of factors, one of which is Chelsea’s ambition.
“I’m waiting for new players next season. I want good players, because I want to win the Premier League next season,” he said in May.
Although he said he is happy at Chelsea, he has been linked with a move to Real Madrid for a long time and according to the Mail, the Champions League winners will now formalise their interest.
Since arriving from Lille in 2012 for £32m, Hazard has become one of the club’s most important players, winning two Premier League titles, the FA Cup, League Cup and Europa League.
His displays at the end of the 2014/15 title winning season also brought him individual glory as he won both the Football Writers and Players’ Player of the Year awards.