The 27-year-old Cagliari defender was linked with a switch to the Saints over the summer, but a deal failed to materialize after Dejan Lovren’s arrival.
After making a bright start to the season, the South Coast club have slipped a little of late, with defensive issues having contributed to some poor results.
Astori is seen as the ideal man to bolster their option, with a move in the coming weeks being mooted.
The Italian ace has been at Cagliari for six years, and has attracted much interest throughout that time.
The likes of AC Milan are rumoured to be tracking him, but Southampton are hopeful that the lure of life in the Premier League may be enough to put them ahead of more illustrious rivals in the race for the enforcer.
Cagliari are reportedly ready to listen to respectable offers for their star man, but it remains unclear as to what value they are looking for.
Astori has ambitions of representing the Azzurri at the World Cup, and may find his chances increasing with a big move.