Speculation has intensified in recent weeks that Mourinho could replace Louis van Gaal at Old Trafford as an underwhelming campaign for the Dutchman continues.
And, should the Portuguese indeed take over at United, Varane is expected to be high on his list of transfer targets.
The France international arrived at the Santiago Bernabeu from Lens during Mourinho's three-year tenure in the Spanish capital and, having become a regular during the past two seasons, the prospect of the 22-year-old leaving is not something Zidane is willing to entertain.
"Of course it is normal Mourinho would want to sign Raphael," he said.
"He knows him well, he brought him here to the club. But I want Varane to stay in Madrid. He is the future of the club."
Madrid, who have taken 13 points from five matches since Zidane replaced Rafael Benitez in January, can close the gap on Atletico Madrid and leaders Barcelona when they host Athletic Bilbao on Saturday.
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Zidane will then make his Champions League coaching bow in the first leg of a round of 16 tie against Roma on Wednesday, with the Frenchman eager to maintain momentum going into the final months of the campaign.
"At the moment the most important thing for me is not the amount of time I am here, but how things are going.
"It is going to be my sixth game, I want to keep the run going and the side playing well.
"As coaches we never know what will happen, you have doubts between games, now we will play every three days so that is all that worries me. It is true it has been a bit more difficult away from home but we have also scored five and six goals at home," he added, referring to heavy victories over Sporting Gijon and Espanyol.
"If we win 1-0, I will be happy. All games are different so we must keep playing to the level we have been and look to the game away at Roma."