The Daily Express reports that Magilton is “under consideration” by the Easter Road hierarchy as they look to make an appointment.
The 49-year-old has had management spells at Queens Park Rangers, Melbourne Victory and Northern Ireland Under-21s as well as his spell at Portman Road.
Magilton, capped 52 times by Northern Ireland, is currently the elite performance director with the Irish Football Association, but is understood to be keen on a return to club management.
The former Oxford United and Southampton midfielder is said to have turned down “a number of English jobs in recent seasons”.
Magilton joins Alan Stubbs, Paul Heckingbottom, Paul Hurst, John Doolan and Simon Grayson as potential candidates for the role.
The Evening News revealed this morning that the Capital club has had around 100 applications for the vacancy.
Hibs are not making any comment while chief executive Leeann Dempster and George Craig, head of football operations, are compiling a shortlist to the point where interviews can be held before recommendations are passed to the board.