Twine is a player that Hull were keen on before he completed a move to Burnley last summer.
Injuries played their part last term as Twine was unable to make an impact at Turf Moor and he finished the campaign with just 14 appearances in the Championship.
Vincent Kompany’s side appear willing to let the midfielder leave this summer and Hull are at the front of the queue.
The Tigers are hopeful that they will be able to finalise a loan move for Twine.
The switch could happen over the coming days, with Twine having indicated to the Championship side that he wants the move.
Moving to Hull will hand Twine the chance to get his career back on track with regular game time.
The midfielder is under contract at Burnley until the summer of 2026 and the Clarets are sure to keep a close eye on how he fares during his loan stint at Hull.