Perk won't sign the extension; it's still a low-ball offer.  He's pretty much forced to enter free agency, which is an unfortunate bi-product of current CBA rules.  In my opinion, if a team is going to have Bird rights, they should be able to extend a player for an amount up to a max contract.  Unfortunately, that's not currently the case.
Anyway, I think Perk will re-sign in OKC, because he's a great fit there.  I can't see a scenario where he accepts an MLE deal, because I think OKC would trump that.  Still, Miami especially would be a great fit for him.  (Um, Boston, too.)