Stauffer is connected to the Oilers and often used as a sounding board with fans before a move is made (He discussed speculation/possibility of Eberle and Hall trades in advance of their departures). I'd wager this is based around a Klefbom trade, myself.
I'm not sure how Edmonton trades Klefbom and ends up a better team for it. Unless they add significantly, they're not going to get a true #1D for him... at which point, the question arises, what's the point? Wouldn't it make more sense to just try to add to what they currently have vs tinkering while not actually addressing needs?
There are things I think Edmonton could do. Add some speed, find a couple guys who might be expendable on their current teams who can play, but also provide a little more (Sheary, Comeau, McGinn, Z.Smith, etc)...
Edmonton has some high end talent, but they need more skilled/quality depth. That's only going to come from two places - kids stepping up or via FA/trade. Edmonton just needs to decide what they have and what they need/want. Tough places for them to be in.