Simon Jones of the Daily Mail reported earlier in the week that the Saints would bid £9.5 million for the Cagliari centre-back, which trumps the £7 million the Reds have offered.
With the state of Liverpool as it is, there's few times where the club would benefit by failing to acquire a player. This is one of those times.
It's hard to envision the 26-year-old Astori having a place in the first team. With Martin Skrtel and Daniel Agger prowling the defense, centre-back is one of the Reds' strongest positions.
Skrtel has struggled at times to adjust to Brendan Rodgers' style, with the Carlos Tevez goal in the meeting between Liverpool and Manchester City in particular sticking out.
On the other hand, the Slovakian defender hasn't played poorly enough on the whole of the season to warrant him sitting on the bench.
Agger, on the other hand, has been one of the club's best players over the past few seasons and seems perfectly suited to pass the ball out of the back. He was the biggest detractor of former manager Roy Hodgson's style as Agger didn't like lumping the ball up the pitch.
Should Astori move to Anfield, he'd likely be at least third on the depth chart. If that would be the case, you have to ask why the club would want to buy him in the first place.
Martin Kelly, Sebastian Coates and Andre Wisdom are all capable of playing centre-back in an emergency situation. There's also Jamie Carragher, who, despite his huge decline, can still fill in on occasions.
Coates has looked shaky at times, but he has all the tools necessary to become a very good player. He just needs more time in the first team. That wouldn't come with Astori's arrival.
While Wisdom and Kelly have spent time at right-back, should Rodgers put them at centre-back, they would work just fine.
Danny Wilson is another long-term option, and although he has failed to assert himself at Liverpool, the Scottish defender is just 21 years old.
Liverpool are a club in rebuild. It would make much more sense to build around the young players already on the roster.
The quartet of youngsters listed, with the exception of Wilson, have all proven they have the potential to start for many seasons to come.
Defenders can have much longer primes than other outfield positions. Regardless, Astori's age is a mark against him because it would also take him some time to adjust to the Premier League.
The Reds want to reach the Champions League, so depth is necessary in order to maintain a high level of play the entire season. It's not enough of a pressing concern at this point to go after a player like Astori.
In addition, they unfortunately don't have the budgetary flexibility to spend £7 million on a centre-back who's already in his mid-20s to simply be in the squad rotation.