The 31 year-old centre-back is currently looking for a new club after officially leaving Brighton at the end of his contract.
The English defender spent seven successful years with the South Coast side before being allowed to depart upon the expiration of his terms.
A significant number of clubs have already approached the central defender regarding his availability ahead of the upcoming campaign.
Several interested parties still harbor serious reservations regarding his overall physical condition after a nightmare year with major injuries.
Webster failed to make a single competitive appearance last season after suffering a devastating anterior cruciate ligament injury during training.
The experienced centre-back is still undertaking his intensive physical rehabilitation program at the training facilities of his former club.
The East London club previously attempted to secure the defender on a temporary loan basis during the January 2025 transfer window.
Former Brighton manager Graham Potter was in charge of the Hammers at the time but a mid-season agreement could not be reached between the clubs.
West Ham United manager Nuno Espirito Santo is desperate to recruit defensive reinforcements following their painful relegation from the top flight.
The Hammers require a significant defensive overhaul to prepare for the unique physical challenges of a grueling season in the Championship.
Wantaway defenders Jean-Clair Todibo and Konstantinos Mavropanos are both actively engineering permanent moves away from the stadium this summer.
Securing an experienced leader like Webster on a free transfer represents a sensible piece of business for the rebuilding club.
The hierarchy must act quickly to convince the player that his long-term future lies in East London as rival contract offers arrive.