Ole Gunnar Solskjaer’s side have long coveted the French centre-half and were reportedly readying an offer ahead of the January transfer window.
But Zidane has insisted the 27-year-old will not be leaving and claimed both he and club chiefs remain desperate for Varane to remain in the Spanish capital.
Real Madrid manager Zinedine Zidane has insisted defender Raphael Varane will not leave
He said: ‘He is part of this club, we were very lucky to be able to bring him to Madrid.
‘He has a great career, he’s achieved a lot since he’s been here. Of course, he is non-transferable for the club, for the coach that I am, for people in general.
‘That’s clear and unambiguous. Now we can’t stop people from talking. They’re not just talking about Varane, but about all the players, Real Madrid ones and others.
‘But for Varane, my position is clear, and it’s the same as the club’s position.’
Classy centre-half Varane has long been coveted by Ole Gunnar Solskjaer’s Manchester United
Sir Alex Ferguson wanted French international Varane in summer 2011, but he moved to Madrid
Solskjaer signed Harry Maguire from Leicester for £80million, but according to the Manchester Evening News the club still want Varane to strengthen their backline.
The 71-cap France international has won four Champions Leagues and three LaLiga titles across more than 300 appearances for the Spanish giants.
Then-Real Madrid manager Jose Mourinho, now at Tottenham, brought Varane to the club in summer 2011 after just one season at senior level for Lens in Ligue 1.
Sir Alex Ferguson was also keen on him, but ended up signing Phil Jones from Blackburn, describing Jones as having the potential to be the Red Devils’ greatest ever player.
Zidane sees his fourth-placed side travel to Villarreal in second for a key clash on Saturday
Jones, 28, has only played twice in the league across the last two seasons for Manchester United and hasn’t played for England for two years, with United reportedly keen to sell in January.
Zidane was speaking ahead of Los Blancos’ crucial clash away at surprise package Villarreal.
Real Madrid in fourth can overtake second-placed Villarreal, managed by former Arsenal boss Unai Emery, with a win at El Madrigal on Saturday afternoon.