The 25-year-old has dropped out of the top flight with Wolves after the club was relegated following a 2-0 defeat to Manchester City a fortnight ago.
It is believed that Jarvis has caught the eye of Saints boss Nigel Adkins, who is prepared to offer £4m for the Englishman this summer, according to The Express.
Jarvis has been at Molineux since 2007.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Manchester CityMan City | 9 | 7 | 2 | 0 | 20 | 9 | 11 | 23 |
| 2 | Liverpool | 9 | 7 | 1 | 1 | 17 | 5 | 12 | 22 |
| 3 | Arsenal | 9 | 5 | 3 | 1 | 17 | 10 | 7 | 18 |
| 4 | Aston Villa | 9 | 5 | 3 | 1 | 16 | 11 | 5 | 18 |
| 5 | Chelsea | 9 | 5 | 2 | 2 | 19 | 11 | 8 | 17 |
| 6 | Brighton & Hove AlbionBrighton | 9 | 4 | 4 | 1 | 16 | 12 | 4 | 16 |
| 7 | Nottingham ForestNott'm Forest | 9 | 4 | 4 | 1 | 11 | 7 | 4 | 16 |
| 8 | Tottenham HotspurSpurs | 9 | 4 | 1 | 4 | 18 | 10 | 8 | 13 |
| 9 | Brentford | 9 | 4 | 1 | 4 | 18 | 18 | 0 | 13 |
| 10 | Fulham | 9 | 3 | 3 | 3 | 12 | 12 | 0 | 12 |
| 11 | Bournemouth | 9 | 3 | 3 | 3 | 11 | 11 | 0 | 12 |
| 12 | Newcastle UnitedNewcastle | 9 | 3 | 3 | 3 | 9 | 10 | -1 | 12 |
| 13 | West Ham UnitedWest Ham | 9 | 3 | 2 | 4 | 13 | 16 | -3 | 11 |
| 14 | Manchester UnitedMan Utd | 9 | 3 | 2 | 4 | 8 | 11 | -3 | 11 |
| 15 | Leicester CityLeicester | 9 | 2 | 3 | 4 | 13 | 17 | -4 | 9 |
| 16 | Everton | 9 | 2 | 3 | 4 | 10 | 16 | -6 | 9 |
| 17 | Crystal Palace | 9 | 1 | 3 | 5 | 6 | 11 | -5 | 6 |
| 18 | Ipswich TownIpswich | 9 | 0 | 4 | 5 | 9 | 20 | -11 | 4 |
| 19 | Wolverhampton WanderersWolves | 9 | 0 | 2 | 7 | 12 | 25 | -13 | 2 |
| 20 | Southampton | 9 | 0 | 1 | 8 | 6 | 19 | -13 | 1 |
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