Udine state prosecutor Antonio Di Nicolo was quoted by the ANSA news agency as saying it was believed "that the player died from a cardiac arrest, the result of natural causes".
Speaking to reporters outside Fiorentina's training ground, Della Valle explained how a meeting for the 31-year-old to sign a new contract was moved from last Thursday due to awful weather conditions.
Fiorentina's game was called off in the morning.
The teams were already on the pitch and warming up for the lunchtime match between Genoa and Cagliari when news broke of Astori's death.
Italian media reported that Astori was found by his team-mates in the early hours in his hotel room in Udine, where the team was staying ahead of an Italian league match.
Astori made his Italian debut in 2011 and played at the 2013 Confederations Cup in Brazil, where he scored against Uruguay.
Astori has been capped 14 times by Italy.
Other Serie A and European clubs and dozens of players sent messages of condolence as did federations such as European soccer body UEFA and global soccer body FIFA, and the global players' union FIFPro.
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"Farewell dear Asto", wrote Buffon in a post on Instagram accompanied by a photo of the two players exchanging pennants before a game between their clubs.
Buffon said he did not usually make a habit of expressing his feelings about others.
In your case, I feel like I'm making an exception to my rule, because you have a young wife and family members who will be suffering, but especially your little girl, she deserves to know that her dad was a decent person. "Congratulations really, you were one of the best sports figures I came across", the 40-year-old legendary goalkeeper posted on Facebook. "It's very hard in this moment to find the right words for the family", Conte told Sky Sports ahead of Chelsea's match against Manchester City.
'I stay very close to his family in this moment because I repeat, he was only 31, it's very hard to explain this situation - his wife, the parents, their daughter'. I stay very close to his family in this moment because he was only 31.
Chelsea coach Antonio Conte has paid tribute to his former player. Prior to that he spent six years at Cagliari and one on loan at AS Roma.
The head of the Italian Olympic Committee and acting head of Serie A, Giovanni Malago, said it was his duty to call off Sunday's matches, which he did at the request of the clubs.
Roberto Mancini told of his "great pain" at the news and AC Milan added: 'A man who loved football and who grew up as a footballer with us.
Serie A's official account tweeted: "Shocked by the tragic news, the whole family of the league Serie A huddles around the family of Davide Astori and Fiorentina. Goodbye captain", said former Italian prime minister Matteo Renzi.