The Premier League champions offered £10m for the former England Under-21 international, according to Sky Sports News.
Keane enjoyed a successful season at Burnley last term, winning the Championship title with the Lancashire outfit and scoring five goals.
He turned out 44 times for Sean Dyche's side during the campaign, featuring in all but one of their league fixtures.
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 | 5 | 4 | 0 | 1 | 10 | 7 | 3 | 12 |
| 6 | Fulham | 6 | 3 | 2 | 1 | 8 | 5 | 3 | 11 |
| 7 | Newcastle UnitedNewcastle | 6 | 3 | 2 | 1 | 8 | 7 | 1 | 11 |
| 8 | Brighton & Hove AlbionBrighton | 6 | 2 | 3 | 1 | 10 | 8 | 2 | 9 |
| 9 | Nottingham ForestNott'm Forest | 6 | 2 | 3 | 1 | 6 | 5 | 1 | 9 |
| 10 | Tottenham HotspurSpurs | 5 | 2 | 1 | 2 | 9 | 5 | 4 | 7 |
| 11 | Manchester UnitedMan Utd | 5 | 2 | 1 | 2 | 5 | 5 | 0 | 7 |
| 12 | Brentford | 6 | 2 | 1 | 3 | 8 | 10 | -2 | 7 |
| 13 | Bournemouth | 5 | 1 | 2 | 2 | 5 | 8 | -3 | 5 |
| 14 | West Ham UnitedWest Ham | 6 | 1 | 2 | 3 | 6 | 10 | -4 | 5 |
| 15 | Everton | 6 | 1 | 1 | 4 | 7 | 15 | -8 | 4 |
| 16 | Leicester CityLeicester | 6 | 0 | 3 | 3 | 8 | 12 | -4 | 3 |
| 17 | Crystal Palace | 6 | 0 | 3 | 3 | 5 | 9 | -4 | 3 |
| 18 | Ipswich TownIpswich | 5 | 0 | 3 | 2 | 3 | 8 | -5 | 3 |
| 19 | Southampton | 5 | 0 | 1 | 4 | 2 | 9 | -7 | 1 |
| 20 | Wolverhampton WanderersWolves | 6 | 0 | 1 | 5 | 6 | 16 | -10 | 1 |
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