HITC Sport understands that Leicester block loan move for the defender.
MK Dons boss Karl Robinson is keen to bolster his defensive options before the loan window shuts later this month and has indentified Moore as his top target.
MK Dons currently find themselves just outside the Championship relegation zone, three points clear of their nearest rival, and Robinson saw Moore's experience as a valuable addition to his squad
Moore spent the first half of the season on loan at Bristol City, making 10 appearances at Ashton Gate before returning to Leicester in January.
The 23-year-old has yet to feature for Leicester in the Premier League so far this season due to the form of the likes of Wes Morgan and Robert Huth at the heart of the high-flying Foxes defence.
A number of clubs, including MK Dons are thought to have made enquiries about taking Moore on loan, but Leicester boss Claudio Ranieri is reluctant to let the England Under-21 international leave in case of injuries.
Ranieri is keen to keep hold all of his players as back-up as they look to maintain their push for the Premier League title.