The 31-year-old club captain passed away at the weekend in a hotel room ahead of his team's Serie A match against Udinese.
Initial reports indicated that the defender had suffered a cardiac arrest from natural causes, but now a criminal investigation has been opened by Italian authorities to look into the possibility of manslaughter.
News circulated that Fiorentina had opted to extend Astori's contract and donate the salary to his partner Francesca and their two-year-old daughter Vittoria.
However, according to Italian journalist Tancredi Palmeri, those reports are untrue.
The reporter tweeted: "The hoax on Fiorentina extending post-mortem contract with Astori has been started by Troll Football India. I said Troll Football India. Really, let's just stay in silence."
Astori earned 14 caps for Italy during his career.