The La Liga outfit believe Casillas could leave the club after a long association and a long-term, Spanish successor is wanted. De Gea is far and above all other candidates on the list after a stellar start to the season at Old Trafford.
Despite struggling for clean sheets under Louis van Gaal, it is widely accepted that De Gea has been one of the few to come out of Manchester United's underwhelming start to the season with any credit.
Forcing a transfer
De Gea's rise to prominence has increased Real Madrid's hopes of signing him, who are hoping to take advantage of what appears to be a chronic case of transition post Sir Alex Ferguson.
Real Madrid believe that De Gea is keen on a move to the Bernabeu and that he would be willing to force through a move if Manchester United can't climb back to the top of the Premier League. As his contract has just 18 months to run, he is in a strong bargaining position.
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Manchester United had hoped to tie De Gea to a new long-term contract, but, so far, any deal remains very much unsigned. Should the situation continue into next year, Van Gaal will be forced to decide whether to cash in or risk losing him for free next summer.
Should De Gea refuse the reported £120,000-per-week offer from Manchester United, Real Madrid will test their resolve with a £20 million offer once the season concludes. Having paid upwards of £18 million to bring him from Atletico Madrid in 2012, it would at least allow the Red Devils to claim back the money invested.
However, De Gea's worth looks well above £20 million. At 23-years-old De Gea has at least a decade at the top level of football and is expected to be, along with Thibaut Courtois, one of the best of his generation.
Manchester United would also have to invest a similar amount to seal an adequate replacement. Only Anders Lindegaard is a realistic in-house option, but it is likely Van Gaal would search for a much more established goalkeeper should De Gea leave.