According to a report in the Daily Mail, West Ham had a bid of around £4m rejected last week but are now ready to go back in with an offer of £4.5m.
Rhodes, 21, scored five for Huddersfield against Wycombe on Friday and has since been the subject of interest from Premier League clubs such as Everton and Tottenham.
Sam Allardyce is confident that the Scotland international prefers a move to Upton Park and is hoping their latest offer with be accepted.
Huddersfield boss Lee Clark has so far been resilient in his attempts to keep hold of the young forward.
Source: DSG
