The Saints are reported to have put a sizeable bid on the table - believed to be around £8million - but they are still some way short of Cagliari's valuation.
Nigel Adkins has made Astori a top target for the January transfer window and may be prepared to dig a little deeper.
Astori's agent claims his client is interested in a switch to St Mary's, but has made it clear that no agreement is close to completion at present.
Renzo Contratto told Sky Sports: "There is an important offer from Southampton but we don't know if Cagliari want to let him go.
"There is a big difference between the bid and the request of the Italian club, which is about £12million.
"If Cagliari were to accept Southampton's offer, Davide would be willing to consider the proposal.
"He would have no problem going to play in a foreign league such as the Premier League."