The player is set to join up with the West Ham squad on a pre-season tour of Austria, and could sign if he proves his fitness.
Barry O'Connor told The Sun: 'West Ham will make a final decision before the next season starts. I cannot discuss what terms could be offered.'
The 35-year-old Spanish midfielder was recently released by Turkish club Besiktas.
Allardyce has already recruited one of his former Bolton players in Jussi Jaaskelainen.
The former Finland international has signed a one-year deal with the newly promoted club.