The Blues star was heavily linked with moves to both Barcelona and Manchester United earlier in the summer as speculation rumbled on over his relationship with the Italian.
Conte was then relieved of his duties in July and replaced with long-term Chelsea target Maurizio Sarri.
Willian now looks set to stay at Stamford Bridge beyond August, although European clubs could swoop in with a bid in the next 18 days.
However, the Brazilian seems confident he will be at the club until Sarri says otherwise.
“I’m here,” he told reporters.
“I’m here because I want to play for Chelsea.
“I will only leave if Chelsea want me to go.”
Asked if he would still be a Chelsea player if Conte was still in charge, Willian responded: “No chance. No chance. No.”
Willian made headlines with a controversial Instagram post after Chelsea won the FA Cup final in May.
The 29-year-old posted a photo of the entire Blues squad posing with the trophy but covered Conte with three trophy emojis.
Speaking about the incident recently, Willian attempted to pass the blame on to his daughter.
“My daughter was playing with my cell phone and she ended up putting those emojis over Conte,” he said
“After the final I got a plane right after the game to come to Brazil.
“When I got here, early in the morning, I was posting some pictures of the champions and, well, I was a bit too tired and ended up posting them like that.”
Conte fell out with a host of Chelsea stars during his controversial two-year tenure in England.
Diego Costa was forced out of the club just months after helping the west London outfit win the Premier League.
And David Luiz found himself frozen out under Conte for a large period last season.
But Willian seems to suggest life under Sarri has Chelsea players excited about the future.
“We are just in the beginning,” he said.
“We know we have to improve.
“Jorginho has played very well. He has a lot of quality and helps our play build up from the back. I think we played very well.
“Now we have to continue like that because next week, we have a great game to play against Arsenal [on Saturday] and we want to win again.”
Chelsea got their Premier League campaign off to a winning start with a 3-0 win over Huddersfield on Saturday afternoon.
The Blues welcome Arsenal to Stamford Bridge this weekend.
