Nainggolan has been linked with Manchester United in recent days, but Pallotta has ruled out losing the 29-year-old, or defender Kostas Manolas, as Roma look to improve on last season's second-placed finish in Serie A.
He told reporters: "Nainggolan and Manolas will stay with us, they are not moving from Roma.
"I think we have the best midfield in Italy. In defence we will improve and we can do that by buying some new players."
The Giallorossi have sold Leandro Paredes, Antonio Rudiger and Mohamed Salah since the end of last season with Pallotta explaining it was due to financial reasons.
He added: "We've made the sales we had to for Financial Fair Play. [New sporting director] Monchi is doing a great job, we have a common plan and we discuss everything together.
"We have a plan for the market, there is a list of players who we are analysing, we have been thinking about some of them for a long time.
"We're thinking about players based on their potential."
Nainggolan has established himself as one of the best central midfielders in Italy after joining Roma from Cagliari, after an initial loan spell, in 2014.