La Viola's centre-back has cropped up on the Russians' radar following his displays this season, and they will look to tempt the Serie A side with a €13m (£10m) offer, according to Izvestia.
Vincenzo Montella is said to have no plans to sell the former Manchester City man, but the offer from Zenit could prove too much to turn down.
Savic has been an ever-present for Fiorentina this season.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Zenit St PetersburgZenit | 25 | 15 | 5 | 5 | 44 | 22 | 22 | 50 |
| 2 | FC KrasnodarKrasnodar | 25 | 14 | 7 | 4 | 41 | 25 | 16 | 49 |
| 3 | Dynamo Moscow | 25 | 12 | 8 | 5 | 42 | 33 | 9 | 44 |
| 4 | Lokomotiv MoscowLokomotiv | 25 | 10 | 11 | 4 | 42 | 34 | 8 | 41 |
| 5 | Spartak Moscow | 24 | 11 | 5 | 8 | 34 | 29 | 5 | 38 |
| 6 | CSKA MoscowCSKA | 24 | 9 | 10 | 5 | 44 | 33 | 11 | 37 |
| 7 | Krylia SovetovKrylia Sovetov | 24 | 10 | 6 | 8 | 42 | 35 | 7 | 36 |
| 8 | Rubin Kazan | 25 | 10 | 6 | 9 | 23 | 30 | -7 | 36 |
| 9 | RostovRostov | 24 | 9 | 7 | 8 | 36 | 38 | -2 | 34 |
| 10 | Nizhny Novgorod | 25 | 8 | 4 | 13 | 24 | 33 | -9 | 28 |
| 11 | OrenburgOrenburg | 25 | 6 | 8 | 11 | 28 | 33 | -5 | 26 |
| 12 | Fakel | 24 | 6 | 8 | 10 | 19 | 27 | -8 | 26 |
| 13 | Ural YekaterinburgUral | 24 | 6 | 6 | 12 | 24 | 38 | -14 | 24 |
| 14 | Baltika | 25 | 6 | 5 | 14 | 25 | 31 | -6 | 23 |
| 15 | Akhmat GroznyAkhmat Grozny | 24 | 6 | 5 | 13 | 23 | 37 | -14 | 23 |
| 16 | Sochi | 24 | 4 | 7 | 13 | 26 | 39 | -13 | 19 |
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