The Brazil ace had been linked with a switch to Manchester United to reunite with his old manager, but he insists he was always going to remain at Stamford Bridge this summer
Mourinho signed Willian as Chelsea manager in 2013, with the pair going on to win the Premier League title together in 2014-15.
However, with Mourinho now at United, the Portuguese tactician was reportedly keen on luring Willian to Old Trafford for the upcoming season.
But Willian says he is happy at Chelsea, having only recently signed a new four-year deal to remain at Stamford Bridge.
"I have a great relationship with Jose, but I am Chelsea. Of course, when someone like him is interested in you then you are happy," Willian said.
"But I signed the contract because I like being a Chelsea player and I see good things here. I signed a new contract and that shows how much I want to stay here.
"But the simple thing is that I want to win titles. To win titles you have to improve and if we can do that then we have a great chance to win titles this season.
"We have the players to do this - and the manager."