The Tigers have agreed a fee with The Latics for the 28-year-old and personal terms have been reached with the player, but King is currently discussing severance payments with the club.
Hull boss Phil Brown is not concerned by the hold up and is adopting a patient approach.
"Our end of the business is done but he still has to tie up a few loose ends at Wigan before the boy can even have a medical to see if he's fit enough to come and join us," said Brown in the Hull Daily Mail.