West Ham's offer was reportedly 50 million Euros (£45m) plus midfielder Pedro Obiang.
Torino are reportedly not open to a sale at all.
They finished seventh last season, one place outside the European spots, and Cairo wants a strong squad led by Belotti to push for the top six.
This is the latest chapter in a frustrating striker search for the Hammers. A move for Maxi Gomez appears to have hit a dead end, The Guardian reported.
Belotti scored 15 goals last season, with his best campaign in 2016/17 when he netted 26.
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