The striker's agent told Goal earlier in August that any potential deal was dependent on Fernando Torres leaving Stamford Bridge before the end of the transfer window.
Goal understands that Torres is now close to sealing a move to AC Milan but Roma maintain that Destro, who scored 13 goals in 20 Serie A appearances last season, will not be the Spaniard's replacement.
"We've not reached out to anybody. He's not for sale, it's completely off the table. I decided that a year ago he wasn't [for sale]," Pallotta told the press.
"We've got a great front line with Destro there. You won't see any crazy things going on [in the transfer market], that's for sure."