Although the source is unreliable, even poor sources don't normally frame things like that unless they're pretty sure it's actually happening. I'd be pretty confident that this is actually getting done, and Rory Smith of the Times has backed TalkSPORT up as well. So don't expect to see Danny featuring against Villa.
If Sturridge really is heading for a medical, we've probably seen the last of him in a Chelsea shirt. The Blues won't want to risk the transfer collapsing by playing him before the deal is finalised. It also means that he'll be out the door as soon as the transfer window opens, which means that we'll be down to one striker in the squad for January. I'd therefore expect his departure to be matched by an incoming player, which could be a Romelu Lukaku recall... or something rather more exotic involving a buyout clause.
Either way, I'd be paying attention once 2013 rolls around.