Positive initial talks took place between the Dons and Gerrard, 36, who will leave LA Galaxy in December.
But the League One side will now continue their search to replace Karl Robinson elsewhere, having already spoken to other candidates.
Gerrard has been linked with Celtic, Inter Milan and a return to Liverpool.
Richie Barker will continue in caretaker charge of the Dons for Tuesday’s match against Chesterfield, with the club in the relegation zone of the third tier of English football.
Gerrard, the fourth-most capped England international, left the MLS side last week, saying he had “options on and off the pitch”.
He left Anfield in May last year, becoming one of the highest-profile English players to move to an American Major League Soccer club.
As well as leading Liverpool to victory in the 2005 Champions League, he won the FA Cup in 2001 and 2006.
The latter game was dubbed ‘The Gerrard Final’ after his two brilliant goals – one in stoppage time – saw his team come from behind to eventually beat West Ham on penalties.
Gerrard, who is currently taking his Uefa A coaching licence, also won three League Cups, the Uefa Cup and the Uefa Super Cup with Liverpool.
Following Robinson’s departure as MK Dons manager, chairman Pete Winkelman said his ambition was to take the club into the Premier League, adding that an important factor in the appointment of the next manager was “playing modern football”.