The Baggies have held talks with Long's advisors over the weekend and are believed to have agreed a fee of between £6million and £7m.
It would surpass the £4.7m Albion paid Real Mallorca for Spanish midfielder Borja Valero three years ago.
West Brom's desire for a new striker is even more pressing as last season's leading scorer, Peter Odemwingie, is battling to overcome an ankle problem.
Albion head coach Roy Hodgson is hoping to sign Long in time for Sunday's Premier League opener with Manchester United at the Hawthorns.
It will be the first monetary outlay of the summer by West Brom after Gareth McAuley, Zoltan Gera and Billy Jones arrived on Bosman free transfers and Ben Foster joined on loan from Birmingham.
Hodgson, who has also signed Martin Fulop from Ipswich, has been pursuing Long all summer after the 24-year-old scored 25 goals last season for Reading.
Championship side West Ham last month failed with a bid thought to total around £7million with add-ons but the Royals are believed to have told Long he can join a top-flight side if the price is right.
Long has also been linked with Celtic, Everton and Newcastle.