The Buckinghamshire side have reached the League One playoffs twice in the last two seasons under manager Karl Robinson, but were beaten at the semi-final stage on both occasions.
Winkelman has admitted that the club cannot develop until they win promotion to the second tier.
"I can't grow the football club if I can't get it promoted. And I'm starting to get very frustrated about that," he told BBC Sport.
"I want to be promoted. It's my biggest thing - the one thing I think needs to happen to the MK Dons."
MK Dons are currently 12th in League One, ten points adrift of the playoff places.