It's not yet an official information as far as I know but I had it from a reliable source: at the end of March / begin of April Testaccio Market stalls will move to the new location in via Galvani (very close to the current market). Since Italian opening dates are often not met I'll try to keep you updated in the coming weeks.
Happy to share here other insights you may have and your comments about the new building too.
From an architectural point of view I already read much criticism...
Anyway I hope that a fully covered market with extended opening hours will contribute to improve quality of the offer in this historical spot for foodies in Rome.