The Saints were tracking the 26-year-old for much of the summer, but a combination of a £10m price tag and the arrival of Dejan Lovren saw a deal pushed aside.
But, Mauricio Pochettino is ready to reignite their pursuit of the defender once the transfer window re-opens.
Despite having the best defensive record in the top tier, the Argentine is keen to bolster his ranks as he sets about gaining qualification for European competition next term.
If signed, Astori would likely complete an impressive back five alongside Lovren, Luke Shaw, Nathaniel Clyne and goalkeeper Artur Boruc.
The Italian international is also wanted by Everton and AC Milan, but Pochettino is hopeful that he can convince him that the South Coast is the right place for him to further his career.
Cagliari are keen to keep their star man, but are aware that a significant offer may be too much to turn away.
Astori is hoping to represent the Azzurri at the World Cup next summer, and may be tempted by guaranteed action in the Premier League ahead of the tournament.
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