Goal.com report that Astori, who has made two appearances for Italy, has already agreed personal terms with Southampton.
Strengthening their defense would not appear to be a priority in January for Liverpool, although there have been lapses at the back on occasion this season.
There has been more news about reported Liverpool target David Villa. Spanish journalist for the Times and AS has claimed that Arsenal boss Arsene Wenger contacted the Barcelona forward to discuss a potential move to the Emirates. However, according to Balague, both Villa and Barcelona are eager for the player to remain where he is until at least the summer.
There had been widespread reports that Villa may be on the move in this month’s transfer window having only been used sparingly since his return from a broken leg at the start of the season.
But Liverpool may well pursue their reported interest for the 31-year-old in the summer, with Villa potentially available for £12 million.
While Liverpool have already brought Daniel Sturridge in this month, manager Brendan Rodgers could well still be seeking to further boost his attacking options. And Liverpool have been linked with one of Sturridge’s former teammates Salomon Kalou.
The Ivorian left Chelsea last summer on a free transfer to Lille, however he has struggled to make an impact in France. Indeed, Lille could be willing to allow Kalou to leave for just €3.5 million (£2.8m) in January, according to Sky Sports. The 27-year-old has spoken of his pleasure at the suggestion that there is interest in him from the Premier League.
“I am flattered with all teams linked with me in England," Kalou said, according to Sky Sports.
"It means I am not a bad player as some people think. Teams such as Liverpool, West Ham, are very good teams."
The fact that Kalou is heading off to the African Cup of Nations could be a stumbling block to any deal this month.
In other news, the Daily Mirror has made the surprising claim that Manchester United boss Sir Alex Ferguson is considering replacing his goalkeeper David de Gea with Liverpool’s Pepe Reina.
There has been talk of late that Reds boss Rodgers could be seeking to bring in another goalkeeper with Reina having been more error-prone of late. Birmingham City’s young keeper Jack Butland has been mentioned as a target.
While the goalkeeping position could well be considered in the summer, it appears unlikely that there will be an overhaul in January.