The Royals are believed to have turned down an initial offer, thought to total around £7million with add-ons, for the 24-year-old.
Long is in demand this summer after hitting 25 goals last term.
West Ham will face competition with Reading having told him he can join a Premier League club, if the price is right, after they failed to gain promotion.
Top-flight sides West Brom, Newcastle and Everton have been linked with moves for Long but Hammers boss Sam Allardyce is hoping to persuade the Republic of Ireland international to stay in the Championship for one more season to spearhead their promotion bid.
West Ham's willingness to spend could also indicate some of their big earners may be on their way out, with Stoke reportedly keen to resurrect their move for Carlton Cole and Scott Parker still a target for Premier League clubs.