Astori was in the city of Udine to prepare for the Sunday match against the local Udinese team.
De Nicolo was quoted Sunday as saying Astori died of "natural causes" after a "cardiac circulatory collapse" - a type of heart attack.
"Genuine compliments, you were one of the best sporting figures I ever came up against".
Davide Astori led the young ACF Fiorentina side with brilliance.
A shirt was also pinned up in his honour, with his ex-team-mates all signing the jersey as they paid their respect to the 14-cap global.
Astori was a man described by Italy team-mate Gianluigi Buffon as "an expression of an old-fashioned world", one where values such as "altruism, elegance, politeness and respect towards others" were more important.
Astori leaves behind longtime girlfriend, model Francesca Fioretti, and their 2-year-old daughter, Vittoria, according to Italian media reports. It's very hard to speak about this tragedy. "He was a great player, especially a fantastic guy". He spent time on loan at Roma and Fiorentina before joining the latter club two years ago on a permanent basis after a six-year tenure with Cagliari.
The reporter tweeted: "The hoax on Fiorentina extending post-mortem contract with Astori has been started by Troll Football India". "This news really hurt me and it's very hard in this moment to find the right words for the family. He was only 31 and it's very hard to explain this situation".
The centre-back would go on to make 174 appearances in Sardinia, and earn his first Italy cap against Ukraine in 2011.