Dons manager Derek McInnes says the midfielder, whose existing deal ends in the summer, has had a long desire to play in England, and will "probably" leave Pittodrie.
McInnes told the club's online video channel RedTV Pawlett, 26, had been made a "good" offer by Aberdeen.
MK Dons are managed by former Hearts head coach, Robbie Neilson.
Since making his Aberdeen debut in early 2009, Pawlett has made more than 200 appearances for the club, scoring 20 goals.
Aberdeen have confirmed Peter Pawlett is likely to sign for MK Dons at the end of the season.