Genoa - who have used six managers in eight different spells since Gian Piero Gasperini departed the club in 2010 – have lost both of their Serie A matches in the current campaign.
They were also knocked out of the Coppa Italia by second-tier Spezia on penalties in the third round.
Liverani, who was appointed in June, has never previously managed and is already under pressure.
But his future is safe, for now at least, according to Preziosi.
"He is a great coach. I'll defend him," he told Odeon TV.
"We've built a good team which is offering opportunities to some young players."
Genoa finished 17th in the Serie A last term.
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