The 21-year-old helped Vincenzo Montella's side avoid relegation from Serie A this season, contributing six goals and three assists in 37 appearances.
Fiorentina finished 16th in the league and just three points clear of the drop zone after failing to win any of their last 14 games.
The Italian attacker was one of the few bright sparks for a team which underperformed since the turn of the year and he has attracted plenty of interest from a number of top sides with his displays in Florence.
Chelsea, Juventus and Napoli have all been keeping a close eye on Chiesa's progress, but no formal offers have yet been submitted.
Inter have also reportedly identified Chiesa as a primary target this summer, with new boss Antonio Conte aiming to bolster his squad at San Siro after being appointed on a three-year deal last week.
The versatile Fiorentina star is currently valued at around €70 million (£62m/$78m), but the club have insisted he will remain at Artemio Franchi Stadium for at least one more year.
The Viola released a statement on their official website on Monday, which reads: "We read continuous news spread by others about the future of Chiesa and where he will play next season.
"The current owner is keen to point out that Federico is a Fiorentina player tied to the club by a long contract and therefore, as far as we are concerned, Chiesa will play in Florence next year and must be the symbol for the team that will be built."
Chiesa has already earned 11 caps for Italy and has been tipped for bright future at the highest level given his unique ability to play on either flank, as a centre-forward or as an attacking midfielder.
He has proved himself as one of the most consistent performers in Serie A in recent years and already has over 100 appearances under his belt for Fiorentina across all competitions.
Chiesa rose through the club's ranks at youth level and it now appears he will continue to lead the line for La Viola heading into a crucial 2019-20 campaign.