The Romans reportedly had a £18.5m offer for the Brazilian turned down during the summer, but they have now returned with another bid.
"I can only say we're going strong and I think I can close a deal with Roma," agent Orlando da Hora told Super Deporte.
Nilmar, 27, scored 17 goals from 44 outings last season.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Real Madrid | 23 | 15 | 5 | 3 | 51 | 22 | 29 | 50 |
| 2 | Atletico MadridAtletico | 23 | 14 | 7 | 2 | 38 | 15 | 23 | 49 |
| 3 | Barcelona | 23 | 15 | 3 | 5 | 64 | 25 | 39 | 48 |
| 4 | Athletic Bilbao | 23 | 12 | 8 | 3 | 36 | 20 | 16 | 44 |
| 5 | Villarreal | 23 | 11 | 7 | 5 | 46 | 34 | 12 | 40 |
| 6 | Rayo Vallecano | 23 | 9 | 8 | 6 | 27 | 24 | 3 | 35 |
| 7 | Real Sociedad | 23 | 9 | 4 | 10 | 20 | 20 | 0 | 31 |
| 8 | GironaGirona | 23 | 9 | 4 | 10 | 31 | 33 | -2 | 31 |
| 9 | Osasuna | 23 | 7 | 10 | 6 | 28 | 32 | -4 | 31 |
| 10 | Mallorca | 23 | 9 | 4 | 10 | 20 | 29 | -9 | 31 |
| 11 | Real BetisBetis | 23 | 7 | 8 | 8 | 27 | 31 | -4 | 29 |
| 12 | Celta Vigo | 23 | 8 | 4 | 11 | 34 | 37 | -3 | 28 |
| 13 | Sevilla | 23 | 7 | 7 | 9 | 25 | 34 | -9 | 28 |
| 14 | Getafe | 23 | 6 | 9 | 8 | 18 | 17 | 1 | 27 |
| 15 | Las PalmasLas Palmas | 23 | 6 | 5 | 12 | 28 | 38 | -10 | 23 |
| 16 | Espanyol | 23 | 6 | 5 | 12 | 22 | 35 | -13 | 23 |
| 17 | Leganes | 23 | 5 | 8 | 10 | 19 | 32 | -13 | 23 |
| 18 | Valencia | 23 | 5 | 7 | 11 | 24 | 37 | -13 | 22 |
| 19 | AlavesAlaves | 23 | 5 | 6 | 12 | 25 | 35 | -10 | 21 |
| 20 | Real ValladolidValladolid | 23 | 4 | 3 | 16 | 15 | 48 | -33 | 15 |
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