The Argentine returned to Genoa in the summer after a three-year spell with Real Zaragoza in the Primera Liga to top the Serie A goal scoring charts with 12 goals.
Milito's brilliant displays caught the eyes of Inter coach Jose Mourinho, whose club inquired about the possibility of buying the 29-year-old hit man.
"There has been contact between Inter and our sporting director, but I told them not to open negotiations," Preziosi told La Gazetta dello Sport.
"I can confirm, and I repeat this for the Genoa supporters, that Milito will not be joining Inter because he is not for sale.
"At the moment we do not have an alternative up front - he is the heart and soul of the team.
Milito, who kicked off his career with Racing in Argentina, played for Genoa for one year in 2004, scoring 33 goals for the club before sealing the Zaragoza move.
"We hold Milito in high regard and have great affection for him.
"He feels good at Genoa and Genoa feel good with him. There is no reason to sell him."