Leeds are searching for a new manager after Neil Warnock stepped down from his role at Elland Road earlier this week.
Magilton, who most recently worked in Australia as head coach of Melbourne Victory having previously enjoyed successful stints with Ipswich Town and Queens Park Rangers, is highly-regarded in coaching circles.
In his first managerial role at Ipswich the 43-year-old just missed out on the play-offs in his second season in charge at Portman Road before moving to QPR.
A number of names have been linked with the Leeds job and former Northern Ireland international Magilton admits he would be interested in the replacing Warnock at Elland Road as he looks to get back into management.
"Of course I would be interested in taking over at Leeds United," Magilton told skysports.com.
"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."