If it's a unique drop from an NPC outside an instance (e.g. Murloc Oracle & Foamspittle Staff) or a quest reward (e.g. Rifle Commander's Eyepatch from Grant Me Revenge) then there is a chance the item will upgrade from green/blue to blue/purple. It is based on RNG, but there is a theory (which I currently support but it's hard to be sure) that you can help this along by not playing an alt or handing in a quest/s for a while. (A week to 5 weeks have been mentioned herein.) The hope is Blizzard has increased the odds in such a case.