Under new manager NigelPearson, the Foxes returned to the Championship at the first time of asking and have made an impressive start to the new campaign.
Retired RAF Group Captain NigelPearson resigned as president of the RBL's Shropshire branch six days before Remembrance Sunday this year, in protest at this new direction, saying the plans are "crazy".
Among the favourites to replace Southgate is former Celtic boss Gordon Strachan, who has been out of work since leaving the SPL side in May, while other names linked are Leicester City manager NigelPearson and former Newcastle and Blackburn manager Graeme Souness.