Leicester have interviewed Joe Royle, Peter Reid and Graeme Souness for the manager's job and the appointment could be made by Saturday.
BBC Sport understands chairman Milan Mandaric is keen to put the new man in charge before this weekend's visit to Preston to resurrect their season.
The Foxes lost a lead and dropped two points at Colchester on Saturday, which left them 14th in the Championship.
And that may be the end for caretaker bosses Frank Burrows and Gerry Taggart.
The pair have been in temporary charge since Gary Megson left the club in August - just three months into his contract after joining from MK Dons.
Gary Megson was then appointed but stayed just six weeks before taking over as manager of Bolton Wanderers.
None of the three candidates to take over are currently in managerial positions.
Royle's last job was at Ipswich and ended in May 2006, while Souness' reign as Newcastle manager finished in February 2006 and Reid left Coventry in January 2005.
Neil Warnock had been linked with the Leicester post but he was recently installed as Crystal Palace boss, while former Wigan manager Paul Jewell is another who is believed to have been considered by Mandaric.