I don't think there is an urgent need for a centre half, as long as Carragher is fourth choice. I remember reading in his book and in an interview that, as much as he loves LFC, if he were to find himself in a position where he isn't getting much game time that he would go elsewhere so that he could play regularly. Now, If Jamie is told that he is behind Coates and even Kelly in the pecking order this season, would he stay true to his word and take a considerable cut from his £90k a week wage here to go and play for relegation fodder (in which he'd probably thrive because they play much deeper and that suits him)? Carra has always struck me as a man of his word, so if Rodgers has told him he isn't going to play very much first team football for us again, he may do the off and then we would indeed need another centre half (who we could pay far less wages to which frees up the funds in the wage bill for more attacking talent). The other scenario of course being if Skrtel goes to City for big bucks. I hope that isn't the case.
I think Gerrard, Aquilani, Henderson and Jonjo are fine options in the midfield going forward, but we do need cover for Lucas; someone that can also play alongside him. If you sell Adam and Spearing for a good, strong, holding midfielder, then I think we look fairly well balanced in the middle with enough numbers, variety and sufficient quality. I think this is an absolute priority over the centre back situation.
Then of course we need a replacement for Dirk out wide and a striker (a poacher ideally). I'd much rather see 2/3 players go out and 3/4 quality players come in than another overhall of the squad that will take another year to gel and leave us off the pace again. It's vital that we make wise decisions in this window so that we can move forward.