Perez told those at the unveiling event, reported by the club website: "It will become an avant-garde and universal icon, one of the great future projects for Real Madrid".
The Premier League side face a race against time to have their ban postponed, with their appeal to be heard on April 11.
Real Madrid's manager has requested the club to sign the Red Devils player, but AS states that taking Pogba away from Manchester United "will be more difficult" for the La Liga giants than getting Eden Hazard.
"So Manchester United particularly certainly need a world-class defender, which he is".
Varane has been linked with moves to Manchester United and Bayern Munich, but it is understood the World Cup victor is first weighing up whether he wants to stay at Madrid before deciding on his next destination. He's ideal for them.
Real Madrid boss Zidane has now plans to lose Varane, who is under contract at the Bernabeu until the summer of 2022.
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"I think he's made a leap with his maturity this year and he's doing well with Castilla".
His second game for the club got off to a hard start as the 20-year-old was forced to pick the ball out of the net in the third minute, after being beaten by a thumping drive by Cucho Hernandez.
"When I see him at press conferences he reminds me of Vicente del Bosque".
"He didn't say anything to me. Located in the heart of Madrid, it will be the best stadium in the world", said club president Florentino Perez.
"There are many things that we are talking about changing next year, but you have to respect all of the players who are here", he continued.
"He found a way to transfer the talent he had as a player to his role as coach and manage a dressing room".