The 27-year-old has been linked with a move back to his homeland for a number of years, with Real's quest to replace standout goalkeeper Iker Casillas having rumbled on since his departure from the club three years ago.
With Real's pursuit of De Gea now seemingly over though following their £38m acquisition of Chelsea goalkeeper Courtois, it appears the Red Devils want De Gea to reaffirm his commitment to the club - by signing a new long-term contract.
The Sun report that fresh terms were offered to De Gea earlier this year, with the club always quietly confident that the Spaniard would refute any interest from Real - despite the fact that his partner continues to live in the Spanish capital.
That's not to suggest that he would have taken Real up on any offer though - with De Gea reportedly keen to repay the loyalty showed to him during his early struggles at Old Trafford.
With the path now clear, United hope that the task to keep De Gea has become that much easier. His current deal expires next June, although the club have the option to extend it by a further 12 months as it stands, and the report suggests that United will look to formalise their offer within the next few weeks.
Signing De Gea to a new deal would surely strengthen United's hand in forthcoming transfer windows, with the Spanish number one having firmly established himself as one of the world's best goalkeepers.