I don't think we have a poor centre midfield. Here's my (very) brief take on them individually:
Dembele - decent defensively, good engine, very good at running with the ball past opponents. Not very agile, gets confused too often once he gets himself in a good position in the final third. Good player
Paulinho - gets in to good positions in the box, good engine, decent technique. Poor tackler, wasteful in front of goal. Good player
Sandro - excellent engine, tough in the tackle, generally good positonally. Very injury-prone, offers zero going forward aside from the odd crackerjack of a strike, sloppy in possession at times. Good player
Capoue - good in the defensive midfield position, decent passer, offers nothing going forward. Decent player
Holtby - great work ethic, good at keeping it ticking, very inconsistent with what he offers in the final third. Decent player
Sigurdsson - a bullet shot. Not a lot else. Limited player
Overall that's a decent array of talent. The main problem is how similar they are, with absolutely none of them offering much competence in the creativity department and, my biggest issue of all...
STATIC
None of them are what you would call great pass and move players. I genuinely don't think any of them can realistically fit in to a system that the likes of Emirates Marketing Project, Liverpool and Woolwich use.
Players like Silva, Fernandinho, Coutinho, Henderson, Ramsey, Wheelchair etc etc. all lack some of our midfielders' tools but are all far, far better equipped to play WITH the ball. Their movement when a teammate has it is for all to see. Ours? I watched today at one stage Chiriches (I think) had the ball and absolutely none of our midfielders offered him an outlet so he had to uncharacteristically hoof it. Dembele in particular is guilty of this when you take in to account his ability.
Modric was a master of this. Having one more destructive type midfielder next to him suited to him perfectly, whether that was Parker or Sandro they complemented one another. We often play with two or three of identical midfielders, none of whom make runs in to good spaces which thus leaves the player who has the ball clueless as to who he can give it to. No cohesion, and that's what I feel is holding us back in the middle of the park. We can dominate some opponents physically but if their players are able to keep the ball well and move then we really struggle to cope.
P.S. No, the answer is not Tom Carroll. Oh how we could have done with Moutinho!