That’s according to former Arsenal defender and BBC Sport pundit Martin Keown, who reckons the Belgian may need the move to be considered as good as Lionel Messi and Cristiano Ronaldo.
Hazard has helped Chelsea win four trophies, including the Premier League on two occasions, since heading to west London from Lille back in 2012.
And his performances for the Blues have seen him widely touted as the next Galactico, with Real considering replacements for the likes of Ronaldo and Gareth Bale.
Speculation over Hazard’s future is mounting again with the winter transfer window set to open tomorrow.
And Keown reckons Conte will be happy to show the 26-year-old the door if he seems keen to move, just as he when Diego Costa fancied a return to Atletico Madrid.
“Conte is the sort of manager as well, if he doesn’t want to stay, then he’ll get him out,” said Keown on Football Focus.
“Perhaps it’s healthy and Hazard needs to go to that other level, that next level, for Messi and Ronaldo.
“He shows flashes of it, something holds him back though, maybe it’s another move to another club.”
Keown’s comments come off the back of Hazard’s father, Thierry, suggesting this week that his son his holding off signing a new deal unless Real swoop for him.
“Eden has rejected a contract extension so he can, if necessary, deal with interest from Real Madrid, where he likes what he sees,” he said.
“At this moment in time, there is no contact. Eden is just one of the parts involved.”
Hazard was left out of the starting line-up for Chelsea’s Premier League showdown with Stoke yesterday.