To be honest the question isn't easy to answer. The top teams in front of us don't have the typical destroying DM that many of you wish that we had.
We don't necessarily need one if we get the personal Brendan wants or would have liked to have at his disposal from the beginning.
If you look at our current personal, I would argue that we'd be fine without having one. But that also means that we got to drop two of our most played players from last season to the bench.
First Martin Skrtel. He is brilliant at what he does - defending. But his instinct to drop deep and not move forward is going to kill us if we don't have a defensive midfielder to occupy the space that he leaves behind (make us look compact)
I would argue that if we play Can instead of Skrtel (and not alongside him for a back three) we could solve that problem easily, it would also make us a poor mans barcelona and we only would have one weakness in our team to sort out for that playing style.
And that weakness is player number two: Simon Mignolet - a brilliant shot stopper with cat like reflexes but his distribution and reading of the game are somewhat not up the standards you need for a possession based style of play. We can't push our backline forward with him between the sticks as it would expose his weaknesses. Something you should never do with your goalkeeper. As it is we have no better option at the club and I don't see us investing in another goalkeeper to dispatch Simon, which I think is fair enough but it also collides with the ideals Brendan has in mind and how he would love to set up his team. (Obviously not hard facts, but how I interpreted his several interviews)
The formation without those two would be looking like this:
--------------------- New Goalkeeper -------------------
------------Can-------------------------Sakho------------
New RB ------------------------------------------ Moreno
--------------------------Allen------------------------------
---------Milner---------------------Henderson------------
Sterling------------------------------------------Coutinho
------------------------Sturridge--------------------------
Without a doubt putting Can there is a big risk and in an ideal world you would replace Allen from the starting lineup but I think this lineup would suit most of our players and Rodgers way more then the way we've been playing lately (including the back three, which is basically set up to accommodate Migs and Skrtel). You could also change either of Henderson/Milner for Coutinho/Lallana for teams that park the bus and put another winger/wide forward out there (Origi, Markovic, Ings - you name it)
But as things stand, we need to deploy Lucas in the postion Allen occupies and drop our defense deep, looking for the counter. And then our main problem isn't the DM, it's the pace we got without Sturridge. So we should maybe adress that first