The 35-year-old is currently a free agent after his contract with Turkish club Besiktas expired in November.
It is unclear whether Hammers manager Sam Allardyce will offer the former Spanish international a deal, according to KUMB.com.
Guti won six La Liga titles and three Champions Leagues during a hugely successful 15-year-spell with Madrid.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| C | Real Madrid | 34 | 27 | 6 | 1 | 74 | 22 | 52 | 87 |
| 2 | GironaGirona | 34 | 23 | 5 | 6 | 73 | 42 | 31 | 74 |
| 3 | Barcelona | 34 | 22 | 7 | 5 | 70 | 43 | 27 | 73 |
| 4 | Atletico MadridAtletico | 34 | 21 | 4 | 9 | 63 | 39 | 24 | 67 |
| 5 | Athletic Bilbao | 34 | 17 | 10 | 7 | 55 | 33 | 22 | 61 |
| 6 | Real Sociedad | 34 | 14 | 12 | 8 | 48 | 35 | 13 | 54 |
| 7 | Real BetisBetis | 33 | 12 | 13 | 8 | 41 | 39 | 2 | 49 |
| 8 | Valencia | 33 | 13 | 8 | 12 | 37 | 38 | -1 | 47 |
| 9 | Villarreal | 33 | 12 | 9 | 12 | 54 | 55 | -1 | 45 |
| 10 | Getafe | 34 | 10 | 13 | 11 | 41 | 47 | -6 | 43 |
| 11 | Osasuna | 33 | 11 | 6 | 16 | 37 | 49 | -12 | 39 |
| 12 | AlavesAlaves | 33 | 10 | 8 | 15 | 31 | 38 | -7 | 38 |
| 13 | Sevilla | 33 | 9 | 11 | 13 | 42 | 46 | -4 | 38 |
| 14 | Las PalmasLas Palmas | 34 | 10 | 7 | 17 | 30 | 43 | -13 | 37 |
| 15 | Rayo Vallecano | 33 | 7 | 13 | 13 | 27 | 42 | -15 | 34 |
| 16 | Mallorca | 34 | 6 | 14 | 14 | 27 | 40 | -13 | 32 |
| 17 | Celta Vigo | 33 | 7 | 10 | 16 | 37 | 50 | -13 | 31 |
| 18 | CadizCadiz | 34 | 4 | 14 | 16 | 23 | 49 | -26 | 26 |
| 19 | Granada | 33 | 4 | 9 | 20 | 36 | 61 | -25 | 21 |
| R | Almeria | 33 | 1 | 11 | 21 | 32 | 67 | -35 | 14 |
| > La Liga Full Table | |||||||||
