The Daily Mail reported on Tuesday evening that the former England manager had already held talks with Leicester last Friday, while Sky Sports said the 69-year-old was interested in the position.

The club remained silent on the reports, with a source saying only that Hodgson is being "sounded out" by Leicester as part of their larger search to fill their coaching vacancy.

The reigning Premier League champions sacked title-winning boss Ranieri last Thursday, and Leicester beat Liverpool 3-1 to climb out of the relegation zone in their first game under Shakespeare on Monday night.

The 53-year-old Shakespeare, who was Ranieri's assistant, remains the top candidate to take the role on a permanent basis until the end of the season and beyond, the source said.

Roy Hodgson has not managed since being let go as England manager after Euro 2016.

Hodgson was England manager until suffering the ignominy of an exit to Iceland at Euro 2016. His contract with the Football Association was not renewed. The 69-year-old, who has stated his desire to return to management, is the latest big name to be linked with Leicester.

Guus Hiddink, who has twice served as Chelsea caretaker boss, and former Manchester City manager Roberto Mancini, who had a short spell as a player with the Foxes, have also been rumoured to be under consideration to succeed Ranieri.

Nigel Pearson, whom Ranieri succeeded as boss in July 2015, has also been linked with a return. However, the circumstances of Pearson's departure -- his son James was dismissed as a player for his role in a racist sex tape in the Leicester owners' homeland of Thailand -- would likely discount that prospect.