Eighteen-year-old Galloway made 13 appearances for the League One outfit during the last campaign, but despite the likelihood of more first-team action, Winkelman has confirmed that the teenager is seeking a move to the Premier League.
Winkelman is quoted by BBC Sport as saying: "We are devastated that Brendan wishes to leave, as we feel our first team is the best place for him at the moment.
"There has been interest from several Premier League sides in Brendan and we fully appreciate the lure of the top flight is enormous.
"We accept that Brendan may have played his last game for the club, but we will remain in discussions with interested parties to ensure that MK Dons receives the best possible deal for one of the country's brightest young talents."
Everton are thought to be one of the Premier League teams interested in signing Galloway.