The 23-year-old, who has three years left on his current deal, has been linked with both Arsenal and AC Milan in recent weeks.
However, Renzo Contratto insists that the Italian international is eager to remain at the Stadio Olimpico next season.
"When a player is sought after by other teams it is always a pleasure. This does not mean though that he will leave," he told Asradioroma.it.
"Mattia wants to stay in Rome and have a starring role with the Giallorossi in both Serie A and the Champions League."
Destro scored 13 goals in 20 games last season to help Roma finish as runners-up behind Juventus in the Serie A table.