The former Liverpool captain is a free agent after LA Galaxy confirmed that the midfielder would not be returning to the club next season.
That led to speculation that Gerrard could return to boyhood club Liverpool in a coaching capacity but Sky Sports News HQ report that MK Dons have offered the 36-year-old their vacant manager’s position after talks earlier this week.
Gerrard, 36, moved to MLS club in the summer of 2015, scoring five goals and providing 14 assists during his two seasons at the club.
The Milton Keynes side are currently without a manager after the departure of Karl Robinson and lie 21st in League One.
The midfielder is in the midst of training for his UEFA A coaching licence, which is usually deemed the minimum requirement for a Football League manager.