Inter was linked with a move for the Italy international over the weekend, with newspaper reports claiming he is wanted by new Nerazzurri boss Antonio Conte.
However, Fiorentina issued a statement, stating the club's conviction that Chiesa will remain in Florence.
"We continue to read news spread by others about the future of Chiesa and where he should play next season," the club statement read. "The current ownership would like to make it clear that Federico is a Fiorentina player who is tied to the club on a long contract, and therefore, as far as we are concerned, he should become the symbolic player for the team that is being built."
Chiesa, 21, is the son of former Italy striker Enrico Chiesa and joined Fiorentina as a schoolboy.
He has established himself in the Viola first team over the past three seasons, recently becoming a regular feature in Roberto Mancini's Italy side.
Fiorentina finished a lowly 16th in Italy's top division last season, while Inter took fourth place before replacing coach Luciano Spalletti with former Juventus, Chelsea and Azzurri boss Conte.
Serie A champion Juventus and Bundesliga winner Bayern Munich have also been linked as possible suitors of Chiesa in recent weeks.