I really think this would go the way of Tomb Raider: Definitive Edition - a graphical overhaul running 1080 60fps.
However...
...Maybe.. just maybe, with what they know about Frostbite and how the engine works (Battlefield 4, DA:I) and as a test for their Next Mass Effect game.... they could use a "next gen" Mass Effect Trilogy as a test for their future game mechanics that they want to put into the next one.
Also, I have no idea how coding would work to go from the PS3/360 era of the Unreal Engine to next gen version of Frostbite. What about lip syncing in the new engine versus old recorded dialogue from the trilogy to PS4/XB1. How is that handled? Lots of questions on how this could be done.
At least for Tomb Raider, it appeared to be a short turn around from "last gen" to next gen. And that also includes creating the multiplayer portion of the game for the PS4/XB1. One could hope they could carry over ME3 multiplayer as well.
Wishful thinking probably.
And BioWare... do not change a thing as it pertains to the story... just incorporate the DLC into the main games.