Hazard came under severe criticism from Sarri last week, who called him out for lacking ambition and leadership traits to become the best player in world football.
The Belgian ace, who's been subject of interest from European champions Real over the past 12 months, subsequently hit back claiming he is a leader but has no interest in improving his current level of performances.
And the Italian tactician has now seemingly conceded that the former Lille star should leave Stamford Bridge if he no longer desires to represent the Premier League giants.
"I hope the opposite. I hope he wants to stay and improve. He has the potential to be the best player in Europe and, sometimes, he’s happy with something less.
"It's my job to improve him and put him in a position to do his best. Sometimes that means I have to say something [critical] in the press to do that. It’s normal. It’s my job."
Hazard has scored 13 goals and registered 10 assists in 29 games across all competitions this season.