The Chiefs duo were selected on opposite sides of Wednesday's Pro Bowl draft, with Poe the choice of Deion Sanders and Smith an assigned pick for Jerry Rice.
Following the draft, Poe told reporters: "I won't be too violent. I know how important Alex is for the Chiefs, but at the same time I'm trying to win the truck they're giving away for the game's MVP. So we'll see how it is.
"I might be gentile. I've got to get the sacks though. I might get him the smoothest way I can, but we'll see about it."