Club president Massimo Cellino has no intention of keeping players at the club against their will and is willing to let the defender lead amid reported interest from Man United
Astori - who was watched by Manchester United manager David Moyes earlier this month as part of a scouting trip to see the club take on Juventus - has five Italy caps to his name and is one of Cagliari's most prized assets following Radja Nainggolan's departure to Roma.
Cellino has been routinely frustrated by his blocked attempts to finance a new stadium for the Sardinia-based club - who have been forced to play home games in Trieste, some 670 miles away.
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"If tomorrow I was asked about Astori or others, I would let them go," Cellino told L'Unione Sarda.
"I cannot protect my boys and so I could give them all away, as was the case for Nainggolan.
"Radja was wanted by PSG and Manchester City, but I succumbed to Roma. He did not want to leave, he had to.
"Zenit were willing to pay €25 million last summer, Juventus offered €20m and were prepared to let me have him until the end of the season (on loan).
"But he could not stay here. How can he grow in a team with no ambition?
"He has gone to Roma. There he will grow with champions like (Francesco) Totti and (Daniele) De Rossi, a good coach and a club that already loves him."