Astori - who has also been linked with Manchester City, Southampton and AC Milan - has five Italy caps to his name and is one of Cagliari's most prized assets after 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.
And with a perceived lack of ambition leading Cellino to let Nainggolan move to Roma this month, he has claimed he would happily allow Astori to follow.
United manager David Moyes was spotted at Cagliari's recent defeat to Juventus, with Astori and Juve midfielder Claudio Marchisio thought to be the subject of his attention.
"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 €25m 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."
