The Spanish goalkeeper has been wanted by Real Madrid for the last few seasons, and knows of his increased worth at Old Trafford.
De Gea was happy to ask for around £300,000-a-week to put him on the same amount as team-mate Paul Pogba.
But he now wants to go beyond that and get another £50,000 on top, making him the second highest paid star at United.
An Old Trafford insider said: “The financial reality has completely altered for David and his people in terms of what his next deal should be worth.
“Last year it was thought getting closer to £250,000 a week would be realistic.
“He has seen United have even deeper pockets that even they first imagined. He is ready to go to a lot more.
“The goalposts have shifted dramatically with what the likes of Sanchez, Pogba, Lukaku and Ibrahimovic are on.
“David knows his next contract could be his last big one and that Real Madrid are still hovering in the background.
“He also knows his true worth to United and that he should be paid commensurate to his standing and the rapidly changing market."