The Rossoblu chief was non-committal when asked if Massimiliano Allegri's side have enquired about the availability of the striker, who has been linked with a host of clubs
The 21-year-old forward, who is co-owned by Siena, is one of this summer's hottest properties in Italy after scoring 12 Serie A goals last season.
Juventus, Inter and Roma have all been credited with an interest in Destro, with reports at the weekend claiming that the Giallorossi were on the verge of securing his services.
However, with Zlatan Ibrahimovic believed to be close to joining Thiago Silva at Paris Saint-Germain, the Rossoneri are in the market for a new forward, with the Italy Under-21 international touted as a strong possibility.
"If [Milan CEO Adriano] Galliani has asked about Destro? I am not saying anything," Preziosi told reporters.
"Destro is a player who is being talked about a lot right now. It is clear that he can be to the liking of several clubs.
"We will see, let's wait for Milan to get their money from PSG."
Genoa and Siena have not yet been able to reach an agreement regarding Destro's ownership, with a new meeting between the two clubs scheduled for Wednesday.
"We will meet with [Siena president] Massimo Mezzaroma to talk about this. We will try to find an agreement, but there is no hurry," Preziosi added.