Unless you can coax someone like Huddleston over from Spurs, or Carrick from us (please!!), you're really stuck for decent English DMF's.
I can see one of three things happening;
1) Wenger signs a foreigner
2) Wenger signs an unknown foreigner
3) Wenger signs no-one
My guess is 3... which is a shame, as you really do need a workhorse/tackler in the middle who has a bit of physical presence.