Magilton, who previously had spells as manager of Ipswich Town, Queens Park Rangers and Melbourne Victory, has said that he would be keen to take over at Elland Road.
"Of course I would be interested in taking over at Leeds United," he told Sky Sports News.
"Leeds United are a massive club in England and it would be a fantastic job for anyone.
"I would relish the chance to manage Leeds and it would be an honour for whoever gets it."
Magilton left his role as manager of Melbourne Victory in 2012 after 12 games in charge.