Crotone consider Giuseppe Sannino, Razvan Lucescu and Walter Zenga after receiving two rejections.
The Calabrian club earned promotion from Serie B this season and will have their first ever top flight campaign.
Coach Ivan Juric opted to walk away in order to take over at Genoa and the race for a replacement has been fraught with difficulty.
First Foggia boss Roberto De Zerbi said no, while today Juventus Primavera youth team tactician Fabio Grosso turned them down as well.
According to Sky Sport Italia, the options for Crotone are now ex-Siena Coach Sannino or Skoda Xhanti manager Lucescu.
Another alternative is believed to be former Sampdoria Coach Zenga.
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