Cifuentes, 43, was sacked at the end of January with Leicester struggling in the bottom half of the Championship.
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With just one point from their last seven league games and a six-point deduction for breaking financial rules while in the Premier League, Leicester are now in the relegation zone.
According to The Telegraph, the troubled club have turned to Rowett, 51, to save them as we head into the business end of the season.
Rowett has been out of work since he was sacked by Oxford United last December having spent one year at the club.