Madrid seemed set to conclude the long-running transfer saga with a deal that would see the Spanish giants pay up to €30 million ($33.5 million, £21.8 million) for De Gea, with Costa Rican international goalkeeper Keylor Navas moving to United.
Initial reports suggested that the documentation needed to formalise the transfer wasn't completed before the Spanish transfer window closed at midnight local time (2200GMT).
However, subsequent reports in the Spanish media claimed Madrid will attempt to demonstrate to the football authorities that all the documentation was in place before the deadline.
De Gea has just one year left on his contract at Old Trafford meaning he could join Madrid for free next year if the transfer doesn't go through now.
The Spanish international hasn't featured in any of United's six games so far this season with manager Louis van Gaal claiming the 24-year-old wasn't focused at the English giants due to Madrid's interest.
The 10-time European champions were in the market for a goalkeeper after Spain captain Iker Casillas ended his 25-year association with the club by moving to Porto in July.
De Gea joined United from Real's city rivals Atletico Madrid in 2011 and despite a shaky start went on to shine, winning the club's fans' and players' player of the year awards for the past two seasons.
However, he refused to sign a new deal with United due to his desire to return to Spain with Real.
A standoff between the two clubs ensued with United also expressing their interest in Real captain Sergio Ramos over the summer before he ended speculation over his future by signing a new five-year deal with Los Blancos.
De Gea's girlfriend, the singer Edurne who represented Spain in the 2015 Eurovision Song Contest, caused a row earlier this year when she slammed Manchester for being ugly.