Ex-Napoli boss Gattuso was appointed as Fiorentina's new manager soon after the 2020/21 Serie A season ended, with his contract set to begin from 1 July.
However, the former AC Milan midfielder has fallen out with the Florence club following a failure to agree on transfer targets, Sky Italy has reported.
Fiorentina are reportedly looking to sign more affordable players compared to those suggested by Gattuso's agent, Jorge Mendes.
It is believed that Mendes was pushing for La Viola to sign the likes of Porto midfielder Sergio Oliveira and Valencia winger Goncalo Guedes, who are valued at €19 million (R319 million) and €25 million (R420 million) respectively, according to Transfermarkt.
"ACF Fiorentina and Mister Rino Gattuso, by mutual agreement, have decided not to follow up on the previous agreements and therefore not to start the next sporting season together," an official statement from the club read.
"The Club immediately set to work to identify a technical choice that would guide the Viola team towards the results that Fiorentina and the City of Florence deserve."
With the clash around the club's transfer strategy having resulted in a mutual termination of in the Italian tactician's contract, ex-Olympique Lyon coach Rudi Garcia and former Leicester City boss Claudio Ranieri are understood to be possible contenders for the job.