However, the Tigers were unable to fund the deal on meaning that the Baggies had no choice but to cancel negotiations.
It appeared as though Albion were set to offload the Republic of Ireland international in order to bring Chelsea's Romelu Lukaku back on loan but the failed move saw the Belgian end up at Everton but sporting and technical director Richard Garlick said that was not the case.
"Hull unexpectedly contacted us on Monday and tabled an acceptable offer for Shane. Given that every player has his price, we discussed it as a club," read a statement released by Garlick.
"We accepted Hull's offer in principle and gave them permission to speak to Shane, but the deal depended on many other factors - including a real reluctance to sell.
"In a phone conversation with Shane's representative, I informed him that Shane was under no pressure to leave. We were definitely not trying to force him out.
"Hull then informed us they could not finance the deal they had tabled and wanted to reduce it to a level that the club would never have accepted in the first place.
"Given that Shane was not a player we were looking to sell, we ended all negotiations with Hull there and then.
"Shane remains a West Bromwich Albion player and we're delighted he's still here.
"He's played an important role in the club's recent progress and we are sure he will make another big contribution this term."