The Baggies are preparing for life back in the Premier League having finished second in the 2009-10 Championship table.
Albion boss Roberto Di Matteo has offloaded Slovenia captain Robert Koren from the club's wage bill to make room for Hunt's arrival, with the Daily Star claiming the new boys have agreed a £4million deal with the Tigers which could rise to £5.5million if the Midlanders stay in the top flight.
Di Matteo won't be happy until the 28-year-old, who has been sidelined since February with a serious foot problem, has signed on the dotted line, though, as arch rivals Wolves are also interested in his services.
Mick McCarthy is keen to reunite Hunt with his Republic of Ireland team-mate Kevin Doyle at Molineux, and had a bid of £5million rejected by Hull in last January's transfer window.
The Tigers' crippling debts and relegation from the Premier League mean they will have to sell for less - but Hunt is believed to favour a move to The Hawthorns, where he would rival Chris Brunt for the left-wing berth.