The news comes after the club sacked Gregorio Manzano after only six months in charge.
Simeone has previously managed in Spain, Italy and his native Argentina.
"We have only made an offer to Simeone," said president Enrique Cerezo.
The 41-year-old is expected to give the board his response by Friday.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Barcelona | 27 | 19 | 3 | 5 | 75 | 27 | 48 | 60 |
| 2 | Real Madrid | 28 | 18 | 6 | 4 | 59 | 27 | 32 | 60 |
| 3 | Atletico MadridAtletico | 28 | 16 | 8 | 4 | 46 | 22 | 24 | 56 |
| 4 | Athletic Bilbao | 28 | 14 | 10 | 4 | 46 | 24 | 22 | 52 |
| 5 | Villarreal | 27 | 12 | 8 | 7 | 49 | 38 | 11 | 44 |
| 6 | Real BetisBetis | 28 | 12 | 8 | 8 | 38 | 35 | 3 | 44 |
| 7 | Mallorca | 28 | 11 | 7 | 10 | 28 | 34 | -6 | 40 |
| 8 | Celta Vigo | 28 | 11 | 6 | 11 | 41 | 41 | 0 | 39 |
| 9 | Rayo Vallecano | 28 | 9 | 10 | 9 | 31 | 31 | 0 | 37 |
| 10 | Getafe | 28 | 9 | 9 | 10 | 25 | 23 | 2 | 36 |
| 11 | Sevilla | 28 | 9 | 9 | 10 | 32 | 37 | -5 | 36 |
| 12 | Real Sociedad | 28 | 10 | 5 | 13 | 25 | 30 | -5 | 35 |
| 13 | GironaGirona | 28 | 9 | 7 | 12 | 36 | 41 | -5 | 34 |
| 14 | Osasuna | 27 | 7 | 12 | 8 | 33 | 39 | -6 | 33 |
| 15 | Espanyol | 27 | 7 | 7 | 13 | 26 | 39 | -13 | 28 |
| 16 | Valencia | 28 | 6 | 10 | 12 | 31 | 46 | -15 | 28 |
| 17 | AlavesAlaves | 28 | 6 | 9 | 13 | 32 | 42 | -10 | 27 |
| 18 | Leganes | 28 | 6 | 9 | 13 | 26 | 43 | -17 | 27 |
| 19 | Las PalmasLas Palmas | 28 | 6 | 7 | 15 | 32 | 47 | -15 | 25 |
| 20 | Real ValladolidValladolid | 28 | 4 | 4 | 20 | 18 | 63 | -45 | 16 |
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