Hazard's future has been a subject of speculation over the close-season, with his superb showing during Belgium's run to the semi-finals of the World Cup again prompting links to Real Madrid.
Sarri replaced Antonio Conte as Chelsea boss early in pre-season and he is looking forward to working with 27-year-old Hazard, who will not feature in Sunday's Community Shield against Manchester City at Wembley after being granted an extended post-Russia 2018 break.
"I talked with him, we didn't talk about this," Sarri said, when asked about Hazard's future plans.
"We talked only about 'can I arrive on Monday instead of Sunday?'
"In this moment there is no problem for Hazard."
Chelsea goalkeeper and Hazard's countryman Thibaut Courtois has also been linked with a move away from Stamford Bridge and Goal understands the Blues are actively searching for a replacement for their current No.1 .
Sarri, though, did not want to dwell on any further potential comings and goings in the transfer window, insisting that he will look to develop his current squad to close the gap on champions Manchester City.
"The table of the last Premier League told me City 100, Chelsea 70 points," he said.
"We have to try to reduce 30 points and I know only one way: to work.
"My job is this, to improve my players. I will try to do it. I don't think that every problem can be resolved by the market."