Imagine you are Cagliari.
On January 6th Saints offer you 8 million pounds. Then four days later, Saints offer you 10 million pounds. Why would you agree to that instead of waiting another four days to see if Saints might up their offer yet again? If Cortese is going to bid against himself, Cagliari will let him do it all transfer window long. Saints will end up paying much more for the player and STILL not get him in any earlier.
If Saints want to get Astori earlier, they need to gain leverage not sweeten the deal. If Cagliari believe that Saints might buy another CB and they will lose that deal then they might sell earlier. Simply offering more money does nothing unless they make an offer so ridiculous that Cagliari can't refuse. Which would be a lot more than 2 million pounds extra.
It looks like some teams are coming in for Radja Nainggolan now. I don't know if Cagliari will still need to sell Astori if they sell Nainggolan. Or at least they may be more hesitant if only because the fans would be pretty unhappy if they sold their two best players.
To badly in the ****, I think they will sell both.