The 24-year-old will only be sold to the Spanish giants as part of a swap deal, with defender Sergio Ramos, 29, joining United.
The club see Real as acting "like bullies" and, with their own revenue soaring, are intent on "slugging it out" with Real for the best players.
De Gea is Real's main summer target.
The Spaniard has one year left on his contract and wants to return to his homeland.
But the Old Trafford club, irritated at the idea Real can cherry-pick their best players, struck first, making two bids for Ramos - the most recent for £28.6m - which have both been turned down.
And speaking on the Spanish club's pre-season tour in Australia, Real Madrid's new coach Rafael Benitez said Ramos, the only Real player United are interested in, was going nowhere.
Victor Valdes
Victor Valdes made only two appearances for United after joining from Barcelona
But while United and manager Louis van Gaal know there is no chance of persuading De Gea to remain at Old Trafford beyond 2016, they are adamant they will not part with their two-time player of the year other than on their terms.
The loss of a potential transfer fee is offset by the knowledge that De Gea can be the difference between winning trophies and not, while in turning down a contract offer from United believed to be around £180,000 a week, the keeper remains on the same £60,000 salary he agreed when he left Atletico Madrid in 2011.
There is also a wider issue. Since the sale of Cristiano Ronaldo for £80m in 2009, United have seen Real sign up a succession of big names, including, in the case of Gareth Bale - who signed from Spurs for a world record £85.3m - players they would like to have signed themselves. The club's hierarchy are eager to see this situation change.
Given Real's more cautious spending policy this summer, there is a belief at Old Trafford that the Spanish club's revenue is increasingly constrained.
The reason for that is a combination of the new method of negotiating TV deals in Spain - Real and domestic rivals Barcelona will no longer be free to negotiate their own contracts and will instead become part of a central pool - the fact most of their major sponsorship deals are already in place, and the fact they have agreed a series of expensive, long-term contracts with their star players.
Meanwhile, Van Gaal has revealed reserve goalkeeper Victor Valdesrefused to play for United's under-21 team and is to be sold.
But the 33-year-old could remain at the club for a while, given statements from his agent that Valdes does not want to leave and the fact that - given his strong Barcelona connection - it may be difficult for him to play for another club in Spain.