Alan Pardew is aiming for a return to the Premier League having turned down offers from clubs in Europe and China, the Independent have reported.
The 56-year-old was dismissed by Crystal Palace last December after a poor run of form, and has since appeared regularly as a pundit for Sky Sports.
He is reportedly happy to continue with his media role until the right job presents itself, despite offers from a number of clubs, including Dynamo Kiev.
Pardew has also been the subject of interest from teams in the Chinese Super League, but is content to remain in England for now.
Leicester and Everton are both searching for new coaches having parted with Craig Shakespeare and Ronald Koeman respectively, although neither are expected to appoint the former West Ham boss.
ESPN reported that Pardew applied for the now vacant managerial role at the King Power Stadium and hoped to speak to the club's owners.
He is expected to bide his time in an attempt to make a return to the Premier League, but he has not ruled out a potential move abroad.
After taking on a punditry role in August, Pardew said: "Having just come out of Premier League management after being in it for the last 10 years, I will hopefully be able to provide a little bit of insight for fans of the game.
"I will have no qualms in saying if there is a substitution that has unbalanced a team. But I would rather talk positively if I can.
"I am not coming on air to make life difficult for managers, I am coming on air to give fans an insight into how managers are thinking. That is something I am well versed in, particularly when managers come under pressure."