Guti is expected to join the Hammers on their pre-season tour of Austria.
Allardyce is ready to hand Guti a two-year contract if the 35-year-old can prove his fitness.
Guti’s represenative in England, 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.”
Guti is available on a free transfer after having been released by Besiktas in November last year.