Twine was a key man in MK Dons’ push for promotion from League One last term and his performances have put him on the radar of Championship sides.
Hull want to take Twine up a division and have been hopeful of being able to do a deal, but now Burnley have entered the mix.
New boss Vincent Kompany is reshaping his Clarets squad and wants to add Twine, with a £4m bid on the cards.
A move to Turf Moor, where Burnley are expected to challenge for promotion to the Premier League, could appeal to the attacking midfielder.
However, another unnamed club are also in the hunt for Twine.
MK Dons are preparing to sell the 22-year-old and are already looking at replacements to come in.
Twine made a total of 49 appearances for MK Dons over the course of the recently concluded campaign, contributing with a whopping 20 goals and 13 assists.
He was also booked just twice.
