Old Trafford officials are unconcerned by the fact the 24-year-old Spaniard has only a year left on his deal and could leave for nothing next summer.
United believe the value of keeping De Gea for another 12 months far outweighs any bid below the world record £32.6million Juventus paid Parma for Gianluigi Buffon in 2001.
They are looking for about £35m before they would even entertain the idea of allowing the former Atletico Madrid man to leave the club.
De Gea was signed by United for £17.8m in 2011, but Real will go in with a first offer as low as £13m. A United source said: ‘The fees mentioned are a long way short. David is a world-class keeper who played a huge role in ensuring we qualified for the Champions League last season. That in itself was worth around £50m to the club.’
In another twist Real fear they are losing control of the Sergio Ramos transfer row after turning down a £35m bid from United.
It is understood that Real president Florentino Perez called Ramos to reassure him that his contract dispute will be sorted soon. But Madrid are concerned that the player has made up his mind to leave and will try to put United off by slapping a £65m price tag on Ramos - who could still be using the situation to force a better deal out of his club. United are keen to keep the Ramos discussions separate to any approach from Real for De Gea.
Original source: United insist on £35m fee for De Gea