According to Matt Law, football news correspondent for the 'Daily Telegraph', Chelsea were worried that Hazard felt unhappy playing under Conte, which could have encouraged him to move elsewhere.
Hazard was heavily linked with Real Madrid over summer after his performances at the World Cup helped Belgium to a third place finish.
The Belgian has made a superb start to the season, with 5 goals and 2 assists in 5 games, including a hat-trick against Cardiff on Saturday.
Law said that Chelsea only became happy that Hazard would stay after Conte was replaced by Maurizio Sarri.
"After Belgium beat England in the World Cup, Hazard gave an interview where he basically said he wanted to go to Real Madrid, Chelsea never really had any worries about him," he said.
15 September 2018
"They were categorical that they were not going to sell him and they knew he was not going to kick off. They were relaxed by the fact he would be fine and they would not suffer any problems.
"They knew he would not be like Thibaut Courtois, who went AWOL to get his move to Madrid over the line. They knew Hazard would not sulk and would be absolutely fine.
"There was no panic at Chelsea and that told you everything about him as a lad and a character.
"Whether the Real Madrid link has gone or comes back, if Hazard stays at Chelsea for the rest of his career I think he will be perfectly happy as long as he is playing in a team that allows him to be free and score he will be happy.
"That was the problem at the end of Conte's tenure. He didn't feel free and there was a real big fear at Chelsea that if Conte had stayed that would be when Hazard would look to go.
"It wouldn't have been about going to a bigger club, it would have been about his own personal happiness. He's got the smile back now."