The Foxes owner chairman Milan Mandaric approached his Dons counterpart Pete Winkelman last week, but Ince will not be joining the relegated Championship side according to his current employers.
The former Manchester United, Liverpool and England midfielder has also been linked with the managerial vacancy at Premier League side Blackburn Rovers.
"Following discussions between the chairman and Paul Ince, it has been decided that Paul will not be pursuing the opportunity at Leicester City," read a club statement.
"Given Paul's success in his emerging managerial career, it can come as no surprise that speculation continues to see his name linked with a number of managerial vacancies.
"In spite of this, as we look forward to the forthcoming League One season, the club remains committed to keeping the hottest young manager in English football at Stadium MK."