Hazard has long been linked with a move to Real Madrid, with manager Zinedine Zidane and club president Florentino Perez both said to be huge admirers.
The Belgium international even refused to rule out a move to the Bernabeu in the future when asked about Real’s interest in the summer.
Chelsea are reportedly keen to tie Hazard down to a new £300,000-a-week contract to fend off potential suitors.
And former Blues defender Le Saux reckons Conte can keep Hazard at Stamford Bridge – as long as he makes the 26-year-old the main man.
When asked whether Chelsea can keep Hazard away from Real Madrid, Betfair ambassador Le Saux said: “I think you just have to resign yourself as a club that there’ll always be suitors out there.
“Especially when you have players playing at the highest level.
“You can never be so presumptuous that you think players will stay at a club for a long period of time as it’s only natural for them to feel like they want to try something new.
“Chelsea will need to make sure Hazard is in the spotlight and, as he’s still young, they have a real opportunity to do so.
“It interested me that he came out and said that Antonio Conte made him better in ‘just a week’.
“It was likely a slight dig at previous management but it does show they have a strong relationship and that counts for so much.”
Hazard played a key part in Chelsea’s Premier League title success last term but has started just two games for the Blues this season after undergoing surgery on an ankle injury in July.
Graeme Le Saux spoke to Express Sport on behalf of Betfair. For more from Le Saux go to https://betting.betfair.com/football/graeme-le-saux