The Royals are believed to have turned down an initial offer of 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 Barclays Premier League club, if the price is right, after they failed to gain promotion.
Attracting attention: several clubs have shown interest in Shane Long (left)
Top-flight sides West Bromwich, Newcastle and Everton have been linked with moves for Long but Hammers boss Sam Allardyce is hoping to persuade the Irishman 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.?
?CLICK HERE TO SIGN UP FOR OUR FREE FANTASY FOOTBALL GAMETime running out for Parker deal, West Ham boss Allardyce tells SpursClub-by-club guide to all the Barclays Premier League summer transfers
Source: Daily Mail
Source: Daily Mail