Blackpool are once again in the market for a new boss after seeing Michael Appleton head for Championship rivals Blackburn Rovers.
They are now looking for their third coach of the season - with Ian Holloway having previously departed for Crystal Palace - and had considered Robinson to be a leading candidate for their vacant post.
MK Dons are reluctant to part with their highly-rated young boss, though, and have snubbed Blackpool's advances.
A statement released by the League One promotion hopefuls read: "It comes as no surprise that Karl's name is once again touted for one of the top managerial positions in the Championship as his bold and stylish brand of football has invited plenty of talk in the industry.
"Since being appointed at stadium:mk as the youngest manager in the Football League, Karl has guided our side to back-to-back play-off campaigns, broken a number of Club records and only yesterday (Tuesday) he created history by leading our Club into the fourth round of the FA Cup for the first time.
"Karl is an ambitious, bright young manager and he is firmly focused on realising MK Dons' dream of Championship football.
"Following discussions between Karl and the Chairman, the Club have turned down an approach from Blackpool to speak to Karl regarding the managerial vacancy at Bloomfield Road.
"Karl remains committed to the players, staff and, most importantly, the fans at Milton Keynes Dons, and will be looking to take the Club from strength to strength by continuing to write new chapters in its history books."