The 29-year-old cleared the air after Chelsea's 2-0 Community Shield defeat by Manchester City under new coach Maurizio Sarri.
"I've always made it very clear that I've always been very happy playing for Chelsea. I never said that I want to leave the club," Willian told reporters.
Willian returned late from his close season break and only joined his team mates at the club's training ground four days before the Community Shield clash at Wembley Stadium.
Former Napoli boss Sarri, who replaced Conte last month, had said he had no problem with Willian and hoped to keep him at the club as he sets about putting his stamp on the team.
"This is a new era, with a new manager and I've had a good conversation with him. I hope we can enjoy a lot of victories," Willian said.
Chelsea, who are looking to improve on their fifth-placed finish last season, kick off their league campaign with a trip to Huddersfield Town on Aug. 11.
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Amlan Chakraborty)
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