Speculation over the Spain international's future has emerged again this week, with the 26-year-old telling AS that "nobody knows the future" when asked about a possible move to the Santiago Bernabeu.
Madrid president Florentino Perez subsequently suggested that "someone was messing around" with De Gea and insisted that any transfer discussions would not start until the end of the season.
De Gea came close to joining Madrid in August 2015 as part of an exchange deal involving Keylor Navas, only to see the move fall through, sparking a public row between the hierarchy of the two clubs.
Mourinho is adamant that De Gea, who signed a new four-year contract with the option for a fifth year weeks after that collapsed transfer, is happy at Old Trafford but is confident there will be no underhand tactics should Madrid come forward with another approach.
"I am not going to speak about hypothetical things," the former Los Blancos coach said. "The only thing that is real is that he is my player. I am happy with him, I know that he is happy with me, and there is absolutely nothing else.
"With Perez and his right arm Jose Angel Sanchez, they are some of the people in football that I can say I did not work for them and then it is over.
"I can say that we are friends forever, big friends. I like them a lot. Friends speak. Friends are open, friends are honest.
"So if at the end of the season I want one of their players or they want one of our players we will not do it through the press that we are going to exchange messages.
"We will be very direct. So they are one of the clubs that I am not worried about at all."
Mourinho had earlier backed comments from executive vice chairman Ed Woodward, who said that he did not expect a significant turnover of players in the next transfer window.
The Portuguese does, however, have targets in mind and he is confident that they are attainable players.
"I know the players I want," he said. "I am not going to tell Mr Woodward and [United owners] the Glazers 'bring me [Lionel] Messi'. I know exactly what I want and I know what I want is possible."