The European champions have been linked with the Belgian for months now, with the galactico shaped hole in their squad yet to be filled since the departure of Cristiano Ronaldo to Juventus last summer.
Hazard admitted back in October that it is his dream to one day play for Madrid and, while he pledged to remain at Stamford Bridge until the end of the season, his future beyond that remains uncertain.
The 28-year-old has played a vital role for Chelsea during the 2018-19 campaign so far, contributing 13 goals and 10 assists across 28 matches for the club.
Speaking ahead of his team's next Premier League encounter against Bournemouth on Wednesday evening, Sarri addressed the Hazard rumours, stating that he should push through a move to the Santiago Bernabeu if he so desires.
"Eden is 28. If he wants to go, I think he has to go," said Sarri, who rested Hazard in Chelsea's FA Cup win over Sheffield Wednesday after his goal-scoring performance in the EFL Cup semi-final against Tottenham.
"Of course, I hope the opposite. I hope he wants to stay here with us and improve. He has the potential to be the best player in Europe at the moment. 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 I have to say something in the pressroom on that. It's normal. It's my job.
"But I was really very happy with the last performance."
The Blues are currently sitting in fourth place in the English top flight, but they face a fight to hold on to that position with Arsenal and Manchester United both also aiming for the final Champions League spot.
Sarri's men have reached the Carabao Cup final and are still in contention to win both the FA Cup and Europa League, but they ultimately slipped out of contention for the Premier League title after an inconsistent winter period.
A lack of goals from the club's main strikers has been one of the team's principal issues, with Hazard shouldering most of the responsibility for goal-getting and at times being asked to play out of position as a false nine.
Hazard will be expected to start once again against Bournemouth, while new signing Gonzalo Higuain is in line to make his Premier League debut for Chelsea.