Fiorentina's Chiesa was a star for Italy in the Under-21 European Championship this summer.
He has attracted interest from Serie A champions Juventus and Champions League winners Liverpool.
Jurgen Klopp is believed to want a younger player who can breathe fresh air to the Reds' attack.
However, Viola owner Rocco Commisso has issued a serious warning to both clubs.
"I will not make the same mistake with Chiesa that was made with Baggio," Commisso told Il Sole 24 Ore (via Metro).
"Roby Baggio was the greatest player ever and they sold him just for money.
“I don’t know if there are any particular clauses in Chiesa’s contract, but as far as I am concerned, he is our champion and I won’t sell him even for €100m (£90m)."
The 21-year-old scored 12 goals in all competitions for Fiorentina last season.
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