Hazard has spent the last six seasons at the London club, winning two Premier League titles and scoring 88 goals from 299 appearances in all competitions.
However, with Chelsea failing to qualify for the Champions League, Hazard is unlikely to commit to a new contract at Stamford Bridge, with his current terms expiring in 2020.
Real Madrid have been frequently linked with an approach and according to The Sun, Manchester City are prepared to go head to head with the Champions League finalists if the 27-year-old signals that he intends to leave West London.
Hazard would cost in excess of £100m, but the report indicates that City would be prepared to meet the Belgian's transfer fee and wage demands to seal a switch this summer.
The playmaker is allegedly waiting on Chelsea to decide on their transfer plans for the summer before making a decision on his future.