Mbappe, 18, is now Europe's most sought-after young talent after a remarkable breakthrough campaign with Monaco last term. Already a full France international, the striker is expected to command a transfer fee that will eclipse the record £89m ($112.3m) United paid for Paul Pogba in August 2016.
Last week – and not for the first time this summer – the teenager graced the cover of Spanish daily AS alongside a headline proclaiming that Real Madrid are to bid €135m for Mbappe.
Arsenal have also been unsuccessful with an opening bid, seeing their €100m offer turned away by Monaco, according to the Daily Telegraph.
On Monday (19 June), Mbappe was the cover star of Spanish daily Marca, who carried a story proclaiming that he had made it known to his representatives that he only wants to play for Los Blancos.
Speaking to Onda Cero later on Monday evening, Perez finally broke Real's silence on the matter. During a wide-ranging interview in which the futures of Cristiano Ronaldo, Alvaro Morata and David de Gea were also discussed, he confirmed Mbappe is very much on the club's radar.
"I've seen very little of Mbappe," he said. "I know he is 18, a very good player, but for the moment he is a Monaco player. I don't know why people say he was born to play for Madrid. I'll tell you if he was born to play for Madrid or not.
"I am sure he will be one of the greats and we are following him. [Zinedine] Zidane's liked him a lot for a while, but it is not true we were close to signing him [a few years ago] because he still hadn't turned 16."
After finishing the 2016-17 campaign outside of the top four amid doubts over the futures of important first-team players, Arsenal manager Arsene Wenger is reportedly ready to revamp his attack ahead of the new season, with Mbappe at the heart of those plans.
According to the Daily Telegraph, the Gunners boss is pushing for Mbappe, Monaco teammate Thomas Lemar and Lyon forward Alexandre Lacazette.