The Hammers sent chief-scout Martin Glover to watch Fuego in action in Valencia's recent match against Rayo Vallecano and he came back glowing with praise over the 30-year-old's performance.
Fuego has started in every game for Valencia so far this season, but the club's financial struggles mean that he could be available in January, regardless of his importance to the team.
Fuego only has 18 months left on his contract, and the La Liga outfit simply cannot afford to risk losing him on a free transfer in 2016, meaning a deal may be agreed.
West Ham are determined to strengthen their squad after making a brilliant start to the Premier League which has left them chasing a Champions League spot.
Sam Allardyce is reportedly targeting three January additions, with Fuego on top of his wishlist as he looks to add further strengthen in depth.
The former Spain youth-international is most comfortable playing a holding role in midfield, but he is also capable at centre-back and this versatility could be vital to the side in the closing stages of the season.
Valencia could also lose Enzo Perez to the Premier League in the January transfer window, with Manchester United reportedly interested in the central-midfielder's services.