The 21-year-old forward is currently on loan from the Gialloblu to Siena and has attracted the interest of Italy's top clubs with his performances for the Tuscan outfit this season.
Indeed, Destro has been heavily linked with Juventus but, according to Tuttosport, Inter are now planning to make a move for a player who came through their youth team ranks before departing for Genoa.
The paper claims that the Nerazzurri are confident of agreeing a deal for the youngster in light of Moratti's close relationship with Preziosi.
However, it is believed that the Genoa supremo will seek a fee in the region of €10 million for Destro, who has netted six times in 21 Serie A appearances so far this term.
Tuttosport also revealed that Moratti and Preziosi hope to resolve the future of Juraj Kucka, the Slovakia midfielder who is co-owned by the two clubs.
The 25-year-old had been expected to move to San Siro in the summer but his poor form this season has cast considerable doubt over the proposed transfer.