The 18-year old has made just 17 competitive appearances for the Dons, since transforming from midfield to defence. Confident in his ball playing ability, he regularly plays the ball out of the defence - a trait that Toffees boss Roberto Martinez has already praised in the player.
The England Under-19 star - who has also appeared for the national Under-17 and Under-18 teams - became the youngest ever player to appear for MK Dons when he made his first-team debut at the age of 15 in 2011.
The youngster was awarded the Football League's Apprentice of the Year, alongside completing his college course, and has been highly praised for his responsible approach to the sport.
The Daily Mail reported that Martinez was tracking the youngster last week, and now NSNO are suggesting that a fee of around £4 million including add-ons has been agreed, and that the player is set to sign in the next few days - despite Martinez currently residing in Brazil for the duration of the World Cup.
Galloway may be just one of MK Dons' highly rated prospects to leave this summer, with 18-year old midfielder Dele Alli - who has been compared to Liverpool legend Steven Gerrard - being tracked by a host of Premier League clubs, including Chelsea, Arsenal, Liverpool and Manchester City.
Alli has made greater strides in the first-team than his teammate, although many believe Galloway is the more naturally talented.
There is no denying that Roberto Martinez has a great record of bringing through youth, with Ross Barkley and John Stones proving their top-flight talent in his first season in charge. Galloway must know that a move to Goodison Park will only further his career, and allow him to unlock his full potential.