Astori, 31, was found dead in his hotel room ahead of Fiorentina's match at Udinese on Sunday, with all Serie A matches consequently postponed.
The cause of the defender's death remains unclear, but an autopsy is due to be conducted while the rest of the squad fly back to Florence.
Astori earned four of his 14 Italy caps under Conte between 2014 and 2016.
"I had him with the national team. It's very hard in this moment to speak about this tragedy.
"He was a fantastic guy. He was a great player but especially a fantastic guy.
"I stay close to his family in this moment because he was only 31 and it's very difficult to explain the situation with his wife, the parents, the daughter."
Conte is the latest in a long line of football figures to have paid tribute to Astori in the wake of his tragic passing.