The Spain stopper signed his new contract but the documents did not reach the professional league's offices by the midnight cut-off on Monday/Tuesday, said several reports without identifying the source of their information.
However, Cadena Ser radio said Real has proof that United sent the paperwork at one minute before midnight and the club are expecting the deal to go through.
Costa Rica keeper Keylor Navas is due to join United as part of the deal if the transfer is completed.
Neither Real nor the professional league could be reached for immediate comment.
If the transfer has failed it will leave De Gea in a difficult position because United coach Louis van Gaal has left him out of the squad for the Premier League club's opening games of the season.
Real want the 24-year-old former Atletico Madrid keeper as a long-term replacement for his Spain team mate Iker Casillas, the former club captain who joined Porto in July.
De Gea was selected last week by Spain for the forthcoming Euro 2016 qualifiers against Slovakia and Macedonia although coach Vicente Del Bosque hinted he could lose his place in the squad if his club situation remained unresolved.
Image: David De Gea
Photograph: Mark Avery/Reuters