The attacker is on-loan at Aston Villa, where he has impressed at times under manager Unai Emery.
Calciomercato.com says Fiorentina have contacted Galatasaray regarding the possibility of signing the 24-year-old.
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There have been no serious negotiations yet, but the interest from the Italian club is described as concrete.
Zaniolo's contract with Galatasaray runs until the summer of 2027.
Villa's loan deal includes a 22.5m buyout option.