Willian, 30, was a reported target for Manchester United and FC Barcelona during the off-season as his relationship with Conte reached a tipping point.
The Brazil international who was on duty at the 2018 FIFA World Cup was reportedly keen on reuniting with former manager Mourinho.
While the Blaugrana saw two separate bids in the region £55m (R990m) rejected by the Blues.
However, former Napoli coach Mauricio Sarri was confirmed as Conte's replacement at the Premier League giants.
And after the opening day 3-0 victory over Huddersfield the Brazilian was asked whether he would have stayed if Conte had not been fired.
"No chance," he told The Evening Standard. "No. I'm here because I want to play for Chelsea.
"I will only leave if Chelsea want me to go."