Mourinho signed Willian from Russian side Anzhi Makhachkala for £30million three years ago and knows he will have to double that fee if he is to attract the player to Old Trafford.
Willian in action against Manchester United at Stamford Bridge
Willian celebrates with Eden Hazard after knocking Manchester City out of the FA Cup
But it is understood Willian, 27, would be keen to link up with his former boss again.
As SunSport reported yesterday, Mourinho is also closing in on a deal to land Swedish superstar Zlatan Ibrahimovic.
And speaking in Los Angeles, where Brazil are preparing for the Copa America, Willian was gushing in his praise for Mourinho.
Willian has been one of the few Chelsea success stories in a disastrous 2015-16 season
He said: "Jose is one of the most successful coaches in the world and Manchester United will be stronger with him as manager.
"I played some of my best football under Mourinho. He is a special coach and I have a great relationship with him.
"Winning the Premier League with him was one of the highlights of my career. I was sad things didn't work out after that."
Jose Mourinho looks set to link up once again with Zlatan Ibrahimovic at Manchester United
Asked if he would like to link up with Mourinho again, Willian said: "I don't think about that. I'm here on Copa America duty with Brazil and I'm not here to do interviews about other things."
However, he did clarify that he had two years left on his contract and, when asked whether he was in talks about a new deal, he said: "That is something my agent deals with."
