Hammers eye Bundesliga midfielder
However they will face competition from Italy and Spain where Juventus are keen, along with Valencia and Sevilla
Spanish publication Estadio Deportivo claim that the Hammers are keeping tabs on the Switzerland international, with his club rating him at £8.6million.
A Hammers source revealed that the player had been scouted at various times this season.
The Germans want the 25-year-old to stay with a potential campaign in the Champions League possible. They are currently in fourth place, one point behind Borussia Dortmund.
Zuber has caught the eye this season after having a hand in five goals during his 15 Bundesliga appearances, scoring three himself and adding another two in assists.