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.

DJ Derek, whose real name is Derek Morris, also appeared at the Big Chill and numerous gigs across the UK.
Avon and Somerset Police confirmed Mr Morris was reported missing on Thursday and a search for him is under way.
Mr Morris's niece, Jennifer Amy, said his disappearance is "completely out of character".
She said: "I've left numerous messages for him and he hasn't got back - if he goes away he always lets me know.
"His friends have been in touch to say he hasn't been in contact.
"We're all extremely worried."
And Bristol's elected mayor, George Ferguson, said on Twitter: "DJ Derek is a legend - I'll do all I can to spread word across #Bristol."
Geoff Barrow, from the band Portishead, has also tweeted his support while Bestival founder and DJ Rob da Bank hoped one of his "favourite ever" DJs would be found.
DJ Derek's disappearance is trending on the social networking site.
Mr Morris launched his DJ Derek career in his mid-30s after working in the accounts department of confectionery firm Cadbury's.
In 2006, he told the BBC's Inside Out that he left the firm after years of "domestic hell" before starting work as a DJ in a Bristol pub.
Over more than 40 years he established himself as a fixture on the city's clubbing scene.
As well as playing at Glastonbury, he has also released his own compilation album and appeared in a Dizzee Rascal video.
In 2012 he won the Lord Mayor's medal for his "outstanding" contribution to the music scene in the city.
Speaking to BBC Radio 4 after he was given the award, he said he finished most sets with the Bob Marley classic One Love.
He said: "It's a perfect signing-off record for a reggae set - let's get together and feel all right. So next time, people, let's get together and feel all right."
He played his final set before retiring at a London show in 2013.
Aberdeen have confirmed Peter Pawlett is likely to sign for MK Dons at the end of the season.
[NEXT_CONCEPT]
A 73-year-old DJ who played sets at Glastonbury has gone missing, his family has said.