The 21-year-old Frenchman is thought to be valued at £20m and has been linked with United as Louis van Gaal to bolster their rearguard.
Chelsea have also staked an interest, with Jose Mourinho, whom he worked with at the Bernabeu, thought to be a long-term admirer.
Although Varane made only his sixth league start in Real's 3-0 win over Getafe yesterday, he is adamant he wants to see out his contract with the La Liga giants.
“I’m 100 percent with the team and feeling happy. I have a contract until 2020,” Varane said.
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Raphael Varane insists he wants to stay at Real Madrid
I’m 100 percent with the team and feeling happy. I have a contract until 2020
Raphael Varane
“I’m calm and when I’ve played, I’ve tried to do well. Sergio Ramos and Pepe play more than me, but I try to do the best I can.
“My knee hasn’t hurt for a year now. I can play every three days without discomfort. My most important objectives are La Liga and the Champions League.
“It’s good to have time to prepare for games. We weren’t worried at 0-0, we wanted to win and had the determination to do so."
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