The 30-year-old Argentine has fallen out of favour at St James' Park this season, making just two appearances in all competitions for the Magpies.
Norwich are now expected to confirm a deal for the player in the coming days, according to Sky Sports News.
Gutierrez has 18 months remaining on his current contract with Newcastle.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Arsenal | 35 | 25 | 5 | 5 | 85 | 28 | 57 | 80 |
| 2 | Manchester CityMan City | 34 | 24 | 7 | 3 | 82 | 32 | 50 | 79 |
| 3 | Liverpool | 35 | 22 | 9 | 4 | 77 | 36 | 41 | 75 |
| 4 | Aston Villa | 35 | 20 | 7 | 8 | 73 | 52 | 21 | 67 |
| 5 | Tottenham HotspurSpurs | 33 | 18 | 6 | 9 | 67 | 52 | 15 | 60 |
| 6 | Manchester UnitedMan Utd | 34 | 16 | 6 | 12 | 52 | 51 | 1 | 54 |
| 7 | Newcastle UnitedNewcastle | 34 | 16 | 5 | 13 | 74 | 55 | 19 | 53 |
| 8 | West Ham UnitedWest Ham | 35 | 13 | 10 | 12 | 56 | 65 | -9 | 49 |
| 9 | Chelsea | 33 | 13 | 9 | 11 | 63 | 59 | 4 | 48 |
| 10 | Bournemouth | 35 | 13 | 9 | 13 | 52 | 60 | -8 | 48 |
| 11 | Wolverhampton WanderersWolves | 35 | 13 | 7 | 15 | 48 | 55 | -7 | 46 |
| 12 | Brighton & Hove AlbionBrighton | 34 | 11 | 11 | 12 | 52 | 57 | -5 | 44 |
| 13 | Fulham | 35 | 12 | 7 | 16 | 51 | 55 | -4 | 43 |
| 14 | Crystal Palace | 35 | 10 | 10 | 15 | 45 | 57 | -12 | 40 |
| 15 | Everton | 35 | 12 | 8 | 15 | 37 | 48 | -11 | 36 |
| 16 | Brentford | 35 | 9 | 8 | 18 | 52 | 60 | -8 | 35 |
| 17 | Nottingham ForestNott'm Forest | 35 | 7 | 9 | 19 | 42 | 62 | -20 | 26 |
| 18 | Luton TownLuton | 35 | 6 | 7 | 22 | 48 | 77 | -29 | 25 |
| 19 | Burnley | 35 | 5 | 9 | 21 | 38 | 70 | -32 | 24 |
| R | Sheffield UnitedSheff Utd | 35 | 3 | 7 | 25 | 34 | 97 | -63 | 16 |
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