Blues manager Andre Villas-Boas has sent scouts to watch the 24-year-old on five occasions this season, according to the Daily Mail.
The Stamford Bridge side are looking for a forward to replace the outgoing Didier Drogba.
Cavani would be expected to cost Chelsea around £35m.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 17 | 13 | 3 | 1 | 40 | 17 | 23 | 42 |
| 2 | Arsenal | 18 | 10 | 6 | 2 | 35 | 16 | 19 | 36 |
| 3 | Chelsea | 18 | 10 | 5 | 3 | 38 | 21 | 17 | 35 |
| 4 | Nottingham ForestNott'm Forest | 18 | 10 | 4 | 4 | 24 | 19 | 5 | 34 |
| 5 | Newcastle UnitedNewcastle | 18 | 8 | 5 | 5 | 30 | 21 | 9 | 29 |
| 6 | Bournemouth | 18 | 8 | 5 | 5 | 27 | 21 | 6 | 29 |
| 7 | Manchester CityMan City | 18 | 8 | 4 | 6 | 30 | 26 | 4 | 28 |
| 8 | Fulham | 18 | 7 | 7 | 4 | 26 | 23 | 3 | 28 |
| 9 | Aston Villa | 18 | 8 | 4 | 6 | 26 | 29 | -3 | 28 |
| 10 | Brighton & Hove AlbionBrighton | 18 | 6 | 8 | 4 | 27 | 26 | 1 | 26 |
| 11 | Brentford | 18 | 7 | 3 | 8 | 32 | 32 | 0 | 24 |
| 12 | Tottenham HotspurSpurs | 18 | 7 | 2 | 9 | 39 | 26 | 13 | 23 |
| 13 | West Ham UnitedWest Ham | 18 | 6 | 5 | 7 | 23 | 30 | -7 | 23 |
| 14 | Manchester UnitedMan Utd | 18 | 6 | 4 | 8 | 21 | 24 | -3 | 22 |
| 15 | Everton | 17 | 3 | 8 | 6 | 15 | 22 | -7 | 17 |
| 16 | Crystal Palace | 18 | 3 | 8 | 7 | 18 | 26 | -8 | 17 |
| 17 | Wolverhampton WanderersWolves | 18 | 4 | 3 | 11 | 29 | 40 | -11 | 15 |
| 18 | Leicester CityLeicester | 18 | 3 | 5 | 10 | 22 | 40 | -18 | 14 |
| 19 | Ipswich TownIpswich | 18 | 2 | 6 | 10 | 16 | 33 | -17 | 12 |
| 20 | Southampton | 18 | 1 | 3 | 14 | 11 | 37 | -26 | 6 |
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