Well if we play a 3 man midfield like you were suggesting, Mata couldn't play. If we stick with a 2 man midfield, Fabregas wouldn't be able to play there against any decent level of opposition. I don't think he's a classic number 10 but for me he's much closer to that than he is to the sort of all round CM we'd need in the middle of the probable 4231.
I think we need two as well. I feel we've lacked a holder for years so someone who can shield the back four and play the ball sensibly through to the attacking midfielders is a priority for me. Then someone who can contribute creatively from deep, preferably a box to box player that can chip in with goals or a deep lying playmaker, though both would need a decent level of defensive ability and tactical/positional awareness.
I'm no scout so I can't say for sure what player suits each position, but Carvalho seems to match the first description pretty well. Then there are doubts over when Strootman could next play, but he matches the box to box role. Vidal would be the dream addition and for me Koke would be a perfect player to combine the playmaking and box to box roles, but both are unrealistic.