The Sun reports that Jose Mourinho wants to reunite with Hazard at Old Trafford and is willing to pay up to £90m ($129m) for his services. The Portuguese manager won the title with Chelsea in 2015 and the Belgian formed a key part of his setup. United won't be shy to meeting Chelsea's asking fee, having already broken the English transfer record with a move for Paul Pogba.
The Belgian is stalling on a new £300,000-a-week four-year deal, with the aim of considering his options in the summer. The 26-year-old has two-and-a-half years left on his Blues contract and is understood to be happy at Stamford Bridge.
Real have been monitoring Hazard as a player of interest for some time but are yet to table an official offer, with the club's manager, Zinedine Zidane, a known admirer of the Belgian.
The Belgium international is a key player for the Blues at Stamford Bridge. He has been the club's player of the year on three occasions for the last four years. He has scored eight goals and registered six assists for Antonio Conte's side in all competitions this term.
Real are planning a shake-up of their squad next summer, with Gareth Bale among the names likely to be shown the door. The 12-time European champions could pursue Hazard as a replacement for Bale, whose career in Spain has stalled due to a series of injuries.
United are also on the lookout to add more firepower to their attack and are losing the battle to sign Atletico Madrid stalwart Antoine Griezmann.
Barcelona have emerged as favourites to sign the forward despite reports that Atletico have decided to present a formal complaint to Fifa after it emerged that Barcelona official had met with the Frenchman's family to sound out his potential move to the Nou Camp.
However, despite the speculation, Hazard is happy with his current deal at Chelsea, where his family is taken care of and he can shuttle between Belgium to meet his friends and brothers.
"It's my sixth year [at Chelsea]. I have my family here," he was quoted as saying by The Sun. "My wife and children feel really good. I'm not far from Belgium, so those close to me and my parents or brothers can come quite often.
"I'm at a big club. Almost every year I win a trophy. On the pitch, it's going really well.
"I'm here for now, I'm trying to finish my year as well as possible. After that, I'll have two years on my contract. We'll see what happens."