The Republic of Ireland international, who only arrived at the KC Stadium in January, has emerged as a surprise transfer target for the south-coast club after Southampton's squad was decimated by a host of close-season exits.
Rickie Lambert, Adam Lallana and Dejan Lovren have all joined Liverpool, Luke Shaw made a big-money move to Manchester United and Calum Chambers signed for Arsenal.
But new Southampton boss Ronald Koeman appears to have taken a huge step towards landing Long for a reported £12.5 million, with Bruce confirming a bid has been accepted.
"We'd not been looking to sell Shane but it's a fantastic offer and we've decided to accept it," Bruce told the Hull Daily Mail.
"The challenge is always to become bigger and better and this money will be put towards strengthening again.
"Whether you are Cristiano Ronaldo or Lionel Messi, everyone in football has got their price.
"Myself and the owners didn't want to lose Shane but we accept it's a very good offer, especially when you consider what we paid [roughly £6m] in January.
"I've got no issues. Ever since I walked through the door of this club the board have supported me in every possible way and I'm sure that will be the case as we look to reinvest.
"In an ideal world the money would have come a month ago but it's come now and we'll deal with it."
