Destro has been linked with a possible move away from Roma this summer, with Chelsea and Tottenham both linked with his signature.
Recent reports have suggested Chelsea are stepping up their interest in Destro as a replacement for Fernando Torres, with the Spaniard being lined up for a move to AC Milan.
However, Pallotta insists Italy international Destro is going nowhere before the close of the transfer window next Monday.
"Destro? He's absolutely not for sale and he has never been so," Pallotta told the Italian press.
"We are getting requests because he's a really good player, but we have no intention of selling him.
"He will stay 100%."