"It’s a team that has always fascinated me - just like Premier League clubs in general.
"It’s most likely that I will never coach the Reds, but doing so would represent a unique goal."
Cosmi, who failed to make it as a professional footballer, guided Perugia to Intertoto Cup glory in 2003.
Antonio Conte is the only Italian manager currently in the Premier League, with compatriots Claudio Ranieri and Walter Mazzarri getting sacked last season.
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