The Brazil international is a long-term target for Mourinho at Old Trafford, having previously lifted the Premier League title together in West London three years ago.
Real Madrid and Barcelona were seemingly at the front of the queue to sign Willian, but the 29-year-old's latest comments will only intensify rumours that a move to United is a strong possibility, with the player admitting that he is regularly in contact with Mourinho.
However, in the same interview with ESPN Brasil ahead of Thursday's transfer cut-off point, the former Anzhi Makhachkala ace reaffirmed that his current focus lies only with Chelsea.
"Mourinho is the best manager I've ever worked with. We have a good relationship, we are friends," he said. "Sometimes we talk, we text, we send messages to each other via WhatsApp. He is a great manager, I really enjoyed working with him. I hope I can work with him again someday.
"I don't know if there was any official bid [from Man United], but some things have happened. Also, everything comes out on the internet, too. But Mourinho talks to my agent all the time, he says 'bring him, bring him'. He has never called me, but he always sends me text messages.
"But I am very happy at Chelsea, I want to stay in the club. I also like living in London, it is an amazing city, and my family is well adapted. So yeah, I intend to stay at Chelsea."
Willian returned to action with Chelsea for the final half-hour of Sunday's Community Shield defeat to Manchester City after being given an extended post-World Cup break.