The contract is worth more than £350,000 a week, reports The Times' Paul Hirst.
That would put De Gea near the top of United's food chain. Alexis Sanchez, the club's bread-winner and oft-maligned winger, reportedly makes around £390,000 a week.
De Gea is considering the offer, sources told Hirst, but the 28-year-old would rather be earning what Sanchez makes.
United fear they could lose De Gea on a free transfer if they fail to agree to terms on a new deal. He officially entered the final year of his contract with the Red Devils on July 1.
However, it's believed that De Gea wants to stay in Manchester, according to Stone, where he's spent the past five seasons after joining from Atletico Madrid.
Paris Saint-Germain and Juventus have been linked with the Spanish shot-stopper.