The Spaniard has struggled with the physicality of the Premier League since his 2011 arrival from Atletico Madrid, and Red Devils chief Sir Alex Ferguson is believed to have lost patience with him.
This has alerted Real, who are keen to find a long-term successor to current number one Iker Casillas.
The Spanish national captain is widely thought of as one of the world’s best goalkeepers, but the Bernabeu-based side are aware that at 31-years-of-age, he is not getting any younger.
He has also suffered with injuries and fallen out with manager Jose Mourinho in recent times.
They see de Gea as a genuine option, and are keen to lure him back to La Liga, where he impressed for their local rivals.
United paid Atletico £17m for his signature, and are likely to want to recoup most, if not all, of the fee they parted with.
Real, one of the richest clubs on the planet, would likely be able to meet United’s demands, making a summer transfer a genuine possibility.
If de Gea does move on, Fergie could turn his attention to Stoke’s Asmir Begovic, who has been in fine form for the Potters this term.