According to The Telegraph (via Express), Leicester considers former Burnley boss Sean Dyche and Brentford coach Thomas Frank to be potential options to take over from Rodgers.
Newsonline report that Dyche is currently without a job after he was sacked by Burnley in the second half of last season.
The 51-year-old enjoyed a spectacular spell at Burnley, most notably taking the English club to the UEFA Europa League qualifiers back in 2018.
Frank, meanwhile, led Brentford to a respectable 13th-place finish in the Premier League last season, their first campaign back in the top flight after 74 long years.
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Frank and Dyche would bring very different approaches to Leicester if they are to be appointed.