O’Neill previously managed the Foxes for five years, winning promotion to the Premier League in his first season in 1996, but it is understood the club are yet to approach the Football Association of Ireland with their interest.
Leicester are searching for a permanent successor to Nigel Pearson, who was sacked amid controversial circumstances earlier this month.
O’Neill, understood to be their preferred candidate, is championed by supporters for one of the most sustained periods of stability and success at the club.
Under the Northern Irishman, they won two League Cups in 1997 and 2000, also reaching the final in 1999, and consistently finished in the safety of mid-table in the Premier League.
O’Neill left their previous home at Filbert Street to join Celtic in 2000, where he spent five years and won three SPL titles.
He took over at Aston Villa in 2006 and spent three years at Leicester’s Midlands rivals before a two-year spell as boss at Sunderland.
The 63-year-old was then appointed Republic of Ireland head coach in 2013, with Roy Keane as his assistant. O’Neill has been backed to odds-on favourite with Sky Bet to return as the club’s manager.