With Iker Casillas set to leave the Bernabeu this summer, Real Madrid boss Carlo Ancelotti is desperate to sign a new goalkeeper even though they already have World Cup star Keylor Navas amongst their ranks.
And according to the Express, the former Chelsea boss is adamant on landing De Gea, despite Manchester United insisting that the Spaniard is not for sale.
Although no fee has been discussed, it is believed that Real Madrid are prepared to break the goalkeeper transfer record of £33million that Juventus paid to Parma to secure the services of Gianluigi Buffon in the summer of 2001.
Despite United not being in need of money, they may be tempted to consider the Los Blancos offer if they fail to convince De Gea, who completed a reported £17.8 million switch from Atletico Madrid to Manchester United in the summer of 2011, to sign a new contract.
As the 24-year-old Spaniard's contract is due to expire in the summer of 2016, the Los Blancos will be able to open pre-contract talks with De Gea in little over 12 months time if United fail to offer him a new deal.
Due to this reason, the Red Devils may be tempted to sell De Gea to Real Madrid and make some money out of his transfer rather them let him leave for free in the future.
Meanwhile, Real Sociedad boss David Moyes is reportedly interested in bringing Manchester United youngster Adnan Januzaj to Spain on a short-term loan deal in January.
Moyes, whose side is currently in 14th place in the La Liga, is keen on getting some players on loan in the winter transfer window, and according to the Daily Mail Januzaj is at the top of the former Manchester United boss' shopping list.
"The president has been very good with me and he is going to let me see what I can do," Moyes told the Daily Mail. "My intention is maybe going into the loan market to bring in a couple of players on loan. If I can boost the squad and give everybody a lift then I will try to do that."
The move may be possible as the 19-year-old midfielder has got limited opportunities at Manchester United this season, and manager Louis van Gaal may be willing to let him go so he will be able to get more first team football.