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 | Liverpool | 5 | 4 | 0 | 1 | 10 | 1 | 9 | 12 |
| 2 | Manchester CityMan City | 4 | 4 | 0 | 0 | 11 | 3 | 8 | 12 |
| 3 | Aston Villa | 5 | 4 | 0 | 1 | 10 | 7 | 3 | 12 |
| 4 | Chelsea | 5 | 3 | 1 | 1 | 11 | 5 | 6 | 10 |
| 5 | Arsenal | 4 | 3 | 1 | 0 | 6 | 1 | 5 | 10 |
| 6 | Newcastle UnitedNewcastle | 5 | 3 | 1 | 1 | 7 | 6 | 1 | 10 |
| 7 | Brighton & Hove AlbionBrighton | 4 | 2 | 2 | 0 | 6 | 2 | 4 | 8 |
| 8 | Fulham | 5 | 2 | 2 | 1 | 7 | 5 | 2 | 8 |
| 9 | Nottingham ForestNott'm Forest | 4 | 2 | 2 | 0 | 4 | 2 | 2 | 8 |
| 10 | Tottenham HotspurSpurs | 5 | 2 | 1 | 2 | 9 | 5 | 4 | 7 |
| 11 | Manchester UnitedMan Utd | 5 | 2 | 1 | 2 | 5 | 5 | 0 | 7 |
| 12 | Brentford | 5 | 2 | 0 | 3 | 7 | 9 | -2 | 6 |
| 13 | Bournemouth | 5 | 1 | 2 | 2 | 5 | 8 | -3 | 5 |
| 14 | West Ham UnitedWest Ham | 5 | 1 | 1 | 3 | 5 | 9 | -4 | 4 |
| 15 | Leicester CityLeicester | 5 | 0 | 3 | 2 | 6 | 8 | -2 | 3 |
| 16 | Crystal Palace | 5 | 0 | 3 | 2 | 4 | 7 | -3 | 3 |
| 17 | Ipswich TownIpswich | 5 | 0 | 3 | 2 | 3 | 8 | -5 | 3 |
| 18 | Southampton | 5 | 0 | 1 | 4 | 2 | 9 | -7 | 1 |
| 19 | Wolverhampton WanderersWolves | 5 | 0 | 1 | 4 | 5 | 14 | -9 | 1 |
| 20 | Everton | 5 | 0 | 1 | 4 | 5 | 14 | -9 | 1 |
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