The former BioWare general manager - Aaryn Flynn - mentioned a possible remaster once on NeoGAF. Aaryn Flynn quit BioWare after the release of Mass Effect Andromeda, so I'm not sure if that's still on the table, if it ever was.
https://www.neogaf.com/threads/the-mass-effect-community-thread.616046/page-65#post-137643298
As for transferring to Frostbite 3: That would make it a remake instead of a remaster, and it would be wildly expensive to make. One of the developers on both ME3 and ME Andromeda said in a series of tweets that Frostbite is the worst engine he ever worked with. A lot of the systems that BioWare created for the Mass Effect trilogy were absent from Frostbite 3, which is probably why the end result of ME Andromeda was so unpolished. The result would probably be a lot better if they stuck with the current engine (Unreal Engine 3) and added improvements to that. I'm secretly hoping that EA won't force BioWare to use Frostbite for their next games, but that's not gonna happen.
Edit: A couple of the above mentioned tweets by gameplay designer Manveer Heir (I had to censor some words because of forum guidelines):
"EA would make Frostbite the engine of choice for a text adventure on mobile if they could... it would need 100 engineers to handle what 1 twine team can do"
"I have PTSD from 4+ years of trying to make MEA on Frostbite, AMA"
Frostbite is easily the worst, [bleep], most pain in the [bleep] engine I've ever used in my career, and I shipped Wolfenstein off the Doom 3 tech which was 
"The exact same game design in Unreal vs. Frostbite will take dozens more engineers, money, and time on FB because of the way its architected and how far behind it is from Unreal (unless you are making BF). There is a reason I chose Unreal Engine 4 as my engine for my next project"
So yeah, if there will be a remaster, I expect it would still be on the Unreal Engine.