Brazil international Alisson joined the Reds for £65million last month - a then world record fee for a goalkeeper.
De Laurentiis told the Gazzetta dello Sport: “Roma? They changed a lot and I don't know if that's good.
“I wouldn't have sold Alisson, not even for €100million. I had offered €60million for him but Roma didn't want to sell him to me.
"A little bird told me in the ear a few years ago but if that were so these two teams would not be able to compete in the Champions League."