The bid was thought to be worth an initial £5m, potentially rising to £8m with add-ons.
New Hammers boss Sam Allardyce is believed to have prioritised the signing of 24-year-old Long as he looks to bring in a striker for the new season.
The Republic of Ireland international is in the final year of his contract and has expressed his wish to play in the Premier League.
He has been linked with a host of top flight outfits this summer including West Brom, Everton and Newcastle.
Reading are believed to prefer a move to the Premier League to avoid selling to a Championship rival.