The Spanish giants have long been linked with a move for De Gea, who was named in the PFA team of the year last term, but their opening offer for the player has been rebuffed.
Instead, Man United representatives presented Madrid with a counter offer, which included defender Sergio Ramos as part of a potential deal.
At the end of last season, Louis Van Gaal stated that he hoped De Gea would yet stay at United but this is looking increasingly unlikely.
The player himself gave nothing away when questioned about his United future while away on international duty with Spain earlier this month.
The transfer saga still hangs in the balance. United are certainly a team on the rise and with Champions League football on the cards next year, he could be motivated to stay. However, Madrid would give him the chance to link up with his family and his girlfriend, singer Edurne Garcia.
It may not be long before an agreement is reached but the hope for United fans is that they can get the possible deal for De Gea.