The Daily Express says 18 year-old Galloway has asked to leave the League One club amid interest from a host of Premier League sides.
The Dons, who handed Galloway his debut at 15, will seek a substantial compensation fee for losing the England Under-19 international.
Galloway made 13 appearances for MK Dons last season, scoring in their FA Cup clash against Halifax in November.
The youngster was sent off in his last appearance of the campaign.
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