City assistant manager David Platt is believed to have watched the 19-year-old two weeks ago.
The Premier League champions will put in an initial offer of £8m at the end of the season to test Palace's resolve, according to The Mirror.
However, Liverpool and Swansea City are also thought to be interested in Williams.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 29 | 21 | 7 | 1 | 69 | 27 | 42 | 70 |
| 2 | Arsenal | 28 | 15 | 10 | 3 | 52 | 24 | 28 | 55 |
| 3 | Nottingham ForestNott'm Forest | 28 | 15 | 6 | 7 | 45 | 33 | 12 | 51 |
| 4 | Chelsea | 28 | 14 | 7 | 7 | 53 | 36 | 17 | 49 |
| 5 | Manchester CityMan City | 28 | 14 | 5 | 9 | 53 | 38 | 15 | 47 |
| 6 | Newcastle UnitedNewcastle | 28 | 14 | 5 | 9 | 47 | 38 | 9 | 47 |
| 7 | Brighton & Hove AlbionBrighton | 28 | 12 | 10 | 6 | 46 | 40 | 6 | 46 |
| 8 | Aston Villa | 29 | 12 | 9 | 8 | 41 | 45 | -4 | 45 |
| 9 | Bournemouth | 28 | 12 | 8 | 8 | 47 | 34 | 13 | 44 |
| 10 | Fulham | 28 | 11 | 9 | 8 | 41 | 38 | 3 | 42 |
| 11 | Crystal Palace | 28 | 10 | 9 | 9 | 36 | 33 | 3 | 39 |
| 12 | Brentford | 28 | 11 | 5 | 12 | 48 | 44 | 4 | 38 |
| 13 | Tottenham HotspurSpurs | 28 | 10 | 4 | 14 | 55 | 41 | 14 | 34 |
| 14 | Manchester UnitedMan Utd | 28 | 9 | 7 | 12 | 34 | 40 | -6 | 34 |
| 15 | Everton | 28 | 7 | 12 | 9 | 31 | 35 | -4 | 33 |
| 16 | West Ham UnitedWest Ham | 28 | 9 | 6 | 13 | 32 | 48 | -16 | 33 |
| 17 | Wolverhampton WanderersWolves | 28 | 6 | 5 | 17 | 38 | 57 | -19 | 23 |
| 18 | Ipswich TownIpswich | 28 | 3 | 8 | 17 | 26 | 58 | -32 | 17 |
| 19 | Leicester CityLeicester | 28 | 4 | 5 | 19 | 25 | 62 | -37 | 17 |
| 20 | Southampton | 28 | 2 | 3 | 23 | 20 | 68 | -48 | 9 |
| > Premier League Full Table | |||||||||
