The 29-year-old moved to Spartak just last summer, but it is understood that he is keen on a return to La Liga after failing to settle in Moscow.
According to Marca, Atletico are confident of reaching an agreement this week, with Spartak also open to the possibility of a sale.
Costa has a contract with his current club until 2017.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Barcelona | 14 | 11 | 1 | 2 | 42 | 14 | 28 | 34 |
| 2 | Real Madrid | 13 | 9 | 3 | 1 | 28 | 11 | 17 | 30 |
| 3 | Atletico MadridAtletico | 14 | 8 | 5 | 1 | 21 | 8 | 13 | 29 |
| 4 | Villarreal | 13 | 7 | 4 | 2 | 25 | 21 | 4 | 25 |
| 5 | Athletic Bilbao | 14 | 6 | 5 | 3 | 20 | 13 | 7 | 23 |
| 6 | Osasuna | 14 | 6 | 4 | 4 | 19 | 22 | -3 | 22 |
| 7 | GironaGirona | 14 | 6 | 3 | 5 | 20 | 18 | 2 | 21 |
| 8 | Mallorca | 14 | 6 | 3 | 5 | 13 | 12 | 1 | 21 |
| 9 | Real BetisBetis | 14 | 5 | 5 | 4 | 16 | 16 | 0 | 20 |
| 10 | Real Sociedad | 14 | 5 | 3 | 6 | 11 | 11 | 0 | 18 |
| 11 | Celta Vigo | 14 | 5 | 3 | 6 | 22 | 24 | -2 | 18 |
| 12 | Sevilla | 14 | 5 | 3 | 6 | 13 | 18 | -5 | 18 |
| 13 | Rayo Vallecano | 13 | 4 | 4 | 5 | 13 | 14 | -1 | 16 |
| 14 | Leganes | 14 | 3 | 5 | 6 | 13 | 19 | -6 | 14 |
| 15 | Getafe | 14 | 2 | 7 | 5 | 10 | 11 | -1 | 13 |
| 16 | AlavesAlaves | 14 | 4 | 1 | 9 | 15 | 24 | -9 | 13 |
| 17 | Las PalmasLas Palmas | 14 | 3 | 3 | 8 | 18 | 25 | -7 | 12 |
| 18 | Valencia | 12 | 2 | 4 | 6 | 12 | 19 | -7 | 10 |
| 19 | Espanyol | 13 | 3 | 1 | 9 | 12 | 26 | -14 | 10 |
| 20 | Real ValladolidValladolid | 14 | 2 | 3 | 9 | 10 | 27 | -17 | 9 |
| > La Liga Full Table | |||||||||
