Matias Almeyda has emerged as a surprise contender for the Leicester job.
The long-haired former Argentina midfielder, who played against England at the 1998 World Cup and alongside Tottenham manager Mauricio Pochettino in the 2002 finals, is now the boss of Mexican side Guadalajara.
He previously coaches River Plate and Banfield in his homeland.
Almeyda, 43, spent one season playing in La Liga with Sevilla before spending seven seasons in Italy's Serie A with Lazio, Parma, Inter Milan and Brescia.
Michael Appleton won his first game as caretaker manager against Swansea on Saturday, following the sacking of Craig Shakespeare a week ago.
Manchester United legend Ryan Giggs has also expressed interest in succeeding Shakespeare — as well as the Everton hot-seat, which is vacant after Ronald Koeman was fired on Monday.
He said: "I think you look at those two teams — Leicester being champions two seasons ago, Everton being a fantastic club with a fantastic history —for me these are clubs I would be interested in."