The League One side are still searching for a new manager following the departure of Karl Robinson last month.
Reports had suggested that Lampard was poised to take over at the club having announced he will be leaving MLS side New York City FC once his current contract expires in December.
But ESPN has suggested that the former Blues man declined MK Dons’ approach, with the intent to continue playing for another year before he retires from the sport.
Although Lampard is taking coaches badges in order to become a manager at some point in the future, he currently remains open to joining a new club and has already received a number of offers.
Both LA Galaxy and Orlando have registered their interest in the 38-year-old.
The ex-England international has also been linked with a return to Stamford Bridge to take on a coaching role under current Blues manager Antonio Conte.
But Lampard has no immediate plans to return to Chelsea should he decide to retire.
The player joins Steven Gerrard in searching for a new club after the former Liverpool captain announced he would be leaving LA Galaxy earlier in the week.
The 36-year-old has been linked to a number of sides and The Independent revealed on Friday morning that Inter Milan have made contact with the player in a bid to lure him to the San Siro.