Twine signed for the League One club last summer and immediately impressed for them in his maiden League One season.
The midfielder made 44 league appearances, with a further two in the playoffs as MK Dons fell at the semi-final hurdle, and scored 20 goals and provided 13 assists.
He was named the League One Player of the Season and now the Tigers are looking to snap up the player deemed to be the third tier’s finest this summer.
The Tigers have made a bid of £3m, in addition to add-ons if the deal is accepted, for Twine to the third tier side and it remains to be seen how MK Dons respond.
MK Dons signed the player as a free agent but Swindon Town still have a sell-on clause, to the tune of 20 per cent.
Hull City chairman and owner Acun Ilicali has made it clear his aim for the Tigers to secure promotion to the Premier League and the club are hoping that Twine helps them achieve that goal.
The midfielder has been linked with the Tigers’ Championship rivals West Bromwich Albion but it is Hull who have now tabled a bid.
