Just like it happened to FC Barcelona last summer, Real Madrid and Atlético de Madrid could be banned by FIFA for breaking the rules about the signings of under-age players, and would therefore be disallowed to sign any player in the following two transfer windows.
As José Ramón de la Morena has reported in Cadena Ser show El Larguero, FIFA has already told the Spanish Federation about this ban, and Atlético de Madrid will receive official confirmation soon enough. Surprisingly enough, the report on this issue that is available at Cadena Ser's website does not claim Real Madrid has been received any communication about this issue. Still, this would explain why Real Madrid has signed so many players (Ødegaard, Asensio, Danilo) earlier than usual, and why they are interested in closing the David De Gea deal as soon as possible.
According to Cadena Ser, the ban could be lifted if Joseph Blatter is re-elected for the FIFA presidency, as he could decide to grant amnesty to all teams involved in this issue.