The 21-year-old netted a brace on Friday to help Russia to a 4-1 win over the Czech Republic in their Euro 2012 opener.
CSKA are aware of the Premier League duo's interest in Dzagoev and are preparing to offer the player a new contract, according to The Sun.
Dzagoev has scored six goals in 21 full international appearances.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 15 | 11 | 3 | 1 | 31 | 13 | 18 | 36 |
| 2 | Chelsea | 15 | 9 | 4 | 2 | 35 | 18 | 17 | 31 |
| 3 | Arsenal | 16 | 8 | 6 | 2 | 29 | 15 | 14 | 30 |
| 4 | Nottingham ForestNott'm Forest | 16 | 8 | 4 | 4 | 21 | 19 | 2 | 28 |
| 5 | Manchester CityMan City | 15 | 8 | 3 | 4 | 27 | 21 | 6 | 27 |
| 6 | Aston Villa | 16 | 7 | 4 | 5 | 24 | 25 | -1 | 25 |
| 7 | Bournemouth | 15 | 7 | 3 | 5 | 23 | 20 | 3 | 24 |
| 8 | Fulham | 16 | 6 | 6 | 4 | 24 | 22 | 2 | 24 |
| 9 | Brighton & Hove AlbionBrighton | 16 | 6 | 6 | 4 | 26 | 25 | 1 | 24 |
| 10 | Brentford | 15 | 7 | 2 | 6 | 31 | 28 | 3 | 23 |
| 11 | Newcastle UnitedNewcastle | 16 | 6 | 5 | 5 | 23 | 21 | 2 | 23 |
| 12 | Tottenham HotspurSpurs | 15 | 6 | 2 | 7 | 31 | 19 | 12 | 20 |
| 13 | Manchester UnitedMan Utd | 15 | 5 | 4 | 6 | 19 | 18 | 1 | 19 |
| 14 | West Ham UnitedWest Ham | 15 | 5 | 3 | 7 | 20 | 28 | -8 | 18 |
| 15 | Crystal Palace | 16 | 3 | 7 | 6 | 17 | 21 | -4 | 16 |
| 16 | Everton | 15 | 3 | 6 | 6 | 14 | 21 | -7 | 15 |
| 17 | Leicester CityLeicester | 16 | 3 | 5 | 8 | 21 | 34 | -13 | 14 |
| 18 | Ipswich TownIpswich | 16 | 2 | 6 | 8 | 16 | 28 | -12 | 12 |
| 19 | Wolverhampton WanderersWolves | 16 | 2 | 3 | 11 | 24 | 40 | -16 | 9 |
| 20 | Southampton | 15 | 1 | 2 | 12 | 11 | 31 | -20 | 5 |
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