The Spanish giants will pay an initial sum of £18m for the 24-year-old plus an additional £3.5m based on performances, according to Marca.
De Gea is said to be keen on the move after taking time off to decide where his future lies.
The shot-stopper is expected to become Rafael Benitez's first signing at Real this summer.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 6 | 5 | 0 | 1 | 12 | 2 | 10 | 15 |
| 2 | Manchester CityMan City | 6 | 4 | 2 | 0 | 14 | 6 | 8 | 14 |
| 3 | Arsenal | 6 | 4 | 2 | 0 | 12 | 5 | 7 | 14 |
| 4 | Chelsea | 6 | 4 | 1 | 1 | 15 | 7 | 8 | 13 |
| 5 | Aston Villa | 6 | 4 | 1 | 1 | 12 | 9 | 3 | 13 |
| 6 | Fulham | 6 | 3 | 2 | 1 | 8 | 5 | 3 | 11 |
| 7 | Newcastle UnitedNewcastle | 6 | 3 | 2 | 1 | 8 | 7 | 1 | 11 |
| 8 | Tottenham HotspurSpurs | 6 | 3 | 1 | 2 | 12 | 5 | 7 | 10 |
| 9 | Brighton & Hove AlbionBrighton | 6 | 2 | 3 | 1 | 10 | 8 | 2 | 9 |
| 10 | Nottingham ForestNott'm Forest | 6 | 2 | 3 | 1 | 6 | 5 | 1 | 9 |
| 11 | Bournemouth | 6 | 2 | 2 | 2 | 8 | 9 | -1 | 8 |
| 12 | Brentford | 6 | 2 | 1 | 3 | 8 | 10 | -2 | 7 |
| 13 | Manchester UnitedMan Utd | 6 | 2 | 1 | 3 | 5 | 8 | -3 | 7 |
| 14 | West Ham UnitedWest Ham | 6 | 1 | 2 | 3 | 6 | 10 | -4 | 5 |
| 15 | Ipswich TownIpswich | 6 | 0 | 4 | 2 | 5 | 10 | -5 | 4 |
| 16 | Everton | 6 | 1 | 1 | 4 | 7 | 15 | -8 | 4 |
| 17 | Leicester CityLeicester | 6 | 0 | 3 | 3 | 8 | 12 | -4 | 3 |
| 18 | Crystal Palace | 6 | 0 | 3 | 3 | 5 | 9 | -4 | 3 |
| 19 | Southampton | 6 | 0 | 1 | 5 | 3 | 12 | -9 | 1 |
| 20 | Wolverhampton WanderersWolves | 6 | 0 | 1 | 5 | 6 | 16 | -10 | 1 |
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