According to James Robson of the Manchester Evening News, Real president Florentino Perez is aware he'll have to offer significantly more than the €52.88 million Juventus paid for Gianluigi Buffon in 2001—which remains the world-record fee for a goalkeeper—and believes the nine-figure sum should suffice.
De Gea is contracted to United until 2019, and the Red Devils have the option to extend that another year but are yet to secure him on a more long-term deal, which has been an encouraging sign for Perez.
ESPN's Alex Shaw discussed the need for United to tie him down as a priority:
The 27-year-old was recently asked about the possibility of moving to the Spanish capital, and while he maintained he is content at United, he did not rule it out.
He told El Partidazo de Cope (h/t Robson):
"I don't think Florentino Pérez has my number. I don't know if I'll be the goalkeeper at Real Madrid.
"What I do know is that I'm very happy in Manchester. What I want is to win titles, like every other player.
"There's no lacking in winning titles there (United)—we have to improve. We are a big club, we are not here to take second place. We have to improve and make this club great."
De Gea is a crucial player for United, as noted by football writer Liam Canning:
Losing him would be a disastrous blow for the Red Devils, who already have a mountain to climb as they look to reel in Manchester City after the Sky Blues finished 19 points ahead of them last season.
Madrid may well appeal, though. De Gea has won the Premier League, the UEFA Europa League, the FA Cup and the League Cup once apiece during his seven years at Old Trafford, but in that time Real have won La Liga twice and the UEFA Champions League four times as well as the Copa del Rey.
The Spaniard is one of the best goalkeepers in the world if not the No. 1, and he could be winning much more at the Santiago Bernabeu than he currently is.
If United keep hold of him beyond the summer, they'll need to rectify that situation as quickly as possible if they're to have him in their ranks for the long term.