The Baggies have held talks with Long's advisors over the weekend and are close to agreeing a fee of between £6 million 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.
Hodgson 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 £7m 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 Everton and Newcastle.