The 24-year-old Icelandic international lit up the Eredivisie last season with 24 goals in 23 games after joining from Belgian side Lokeren.
He has continued that rich vein of form with 11 in eight at the start of the new campaign, catching the attention of a few Premier League admirers.
Cardiff City and Newcastle United have both been linked with moves for the 6'2" forward, who could cost between £6m and £8m.
According to The Mirror, the Hammers are the latest club to join the chase, with injury to Andy Carroll leaving Allardyce with just Modibo Maiga and Mladen Petric as the only fit strikers at Upton Park.
Carlton Cole has signed back on until January in a bid to boost the attacking numbers.