The 36-year-old, who only announced his retirement last week, turned down the offer, and now the Dons want to speak to Neilson.
The club said in a statement: "Milton Keynes Dons Football Club can confirm it has made an official approach for Heart of Midlothian's head coach Robbie Neilson with regards to its vacant managerial position.
"The club respects that Hearts has an important fixture with Rangers in the Scottish Premiership on Wednesday evening and, therefore, no further comment will be made until after that match."
Hearts also confirmed that contact has been made, but stressed that Neilson will remain focused on this week's clash against Rangers.
"The club can confirm that MK Dons have made an official approach to Heart of Midlothian in relation to head coach Robbie Neilson," said the Scottish outfit.
"Robbie is aware of the approach but he remains fully focused on the immediate task at hand, which is of course, Rangers at home on Wednesday. No further comment or statement will be made by the club until after this match."
Neilson, who has been in charge of Hearts since 2014, guided the club to the Scottish Championship title in the 2014-15 season.