With Andy Carroll out with injury, the Telegraph report that Sam Allardyce has turned his attention to Peter Crouch.
Stoke City value the England international at £3 million but West Ham refuse to meet Crouch's asking price.
West Ham value the 33-year-old striker at £1 million.
West Ham failed in a bid to secure a free transfer for Samuel Eto'o and with their other prime target Hugo Almeida reportedly not interested in a move to England, Allardyce is running out of time to sign a player capable of leading the Hammers attack.
West Ham kick-off their EPL campaign with a tricky match against rivals Tottenham Hotspurs on August 16.
West Ham managed to complete a league double over the London rivals and will be hoping to have a fit striker available to ensure their EPL season starts off with a win.