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 | 19 | 14 | 4 | 1 | 47 | 19 | 28 | 46 |
| 2 | Arsenal | 20 | 11 | 7 | 2 | 39 | 18 | 21 | 40 |
| 3 | Nottingham ForestNott'm Forest | 19 | 11 | 4 | 4 | 26 | 19 | 7 | 37 |
| 4 | Chelsea | 20 | 10 | 6 | 4 | 39 | 24 | 15 | 36 |
| 5 | Newcastle UnitedNewcastle | 20 | 10 | 5 | 5 | 34 | 22 | 12 | 35 |
| 6 | Manchester CityMan City | 20 | 10 | 4 | 6 | 36 | 27 | 9 | 34 |
| 7 | Bournemouth | 20 | 9 | 6 | 5 | 30 | 23 | 7 | 33 |
| 8 | Aston Villa | 20 | 9 | 5 | 6 | 30 | 32 | -2 | 32 |
| 9 | Fulham | 20 | 7 | 9 | 4 | 30 | 27 | 3 | 30 |
| 10 | Brighton & Hove AlbionBrighton | 20 | 6 | 10 | 4 | 30 | 29 | 1 | 28 |
| 11 | Brentford | 20 | 8 | 3 | 9 | 38 | 35 | 3 | 27 |
| 12 | Tottenham HotspurSpurs | 20 | 7 | 3 | 10 | 42 | 30 | 12 | 24 |
| 13 | Manchester UnitedMan Utd | 20 | 6 | 5 | 9 | 23 | 28 | -5 | 23 |
| 14 | West Ham UnitedWest Ham | 20 | 6 | 5 | 9 | 24 | 39 | -15 | 23 |
| 15 | Crystal Palace | 20 | 4 | 9 | 7 | 21 | 28 | -7 | 21 |
| 16 | Everton | 19 | 3 | 8 | 8 | 15 | 25 | -10 | 17 |
| 17 | Wolverhampton WanderersWolves | 19 | 4 | 4 | 11 | 31 | 42 | -11 | 16 |
| 18 | Ipswich TownIpswich | 20 | 3 | 7 | 10 | 20 | 35 | -15 | 16 |
| 19 | Leicester CityLeicester | 20 | 3 | 5 | 12 | 23 | 44 | -21 | 14 |
| 20 | Southampton | 20 | 1 | 3 | 16 | 12 | 44 | -32 | 6 |
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