The answer? Good god, I hope not.
Cox just signed a monster deal with the Eagles: six year, $102.6 million extension. $36 million is fully guaranteed at signing while $55 million will be fully guaranteed in March 2017. Overall, $63 million is guaranteed for injury. You contract nerds can read more details here.
Are you sure you want to pay Poe now? Not that type of money. In a salary cap world you can't pay multiple players that much money. Justin Houston got a very similar contract: six years, $101 million. The cap goes up every year but not enough to comfortable account for two $100 million contracts. Not to mention Alex Smith and Jeremy Maclin's sizable contracts.
A big difference between the two statistically is sacks. Cox gets twice as many as Poe. Not to say that Poe isn't valuable but Cox seems to be more of a disrupter than Poe.
That said, while it's not a perfect comparison, I do think Poe will clearly benefit from the trickle-down effect of this deal. When the top of the market is set, the level below it is affected too.
I know you're looking for suggested contract numbers for Poe here. I can only guess what those might be because I don't know any talks Poe and the Chiefs have had. Poe is under contract for 2016 and then we'll let the franchise tag help set the market.
2016 fifth year option: $6.1M
2017 franchise tag: $15M (estimated)
2018 franchise tag: $18M (estimated)
Over the course of three years, in my simulation the Chiefs could keep Poe for an estimated cost of $39 million. That, to me, is right around where these negotiations need to start because the Chiefs can unilaterally decide this is how Poe will be paid for the next three seasons (unilaterally ... assuming he shows up and signs it).
The problem with that scenario is that by waiting again the Chiefs are hurting themselves by not having the franchise tag available. What if using the tag on Poe means you lose Eric Fisher in 2017? Or Phillip Gaines the year after that? Or Jaye Howard? Chiefs GM John Dorsey often tries to be flexible but by waiting on Poe (and Houston) the Chiefs have cost themselves.