The big headline for those desperate to see the new hardware is that it's expected to be revealed before E3 - Bloomberg reports that this is to allow major third-parties to showcase a full range of titles during the upcoming event. That means, provided the reports are accurate, any time in the next two weeks.
Manufacturing is expected to begin fully in July, with a targeted launch of September or October, which would also allow the system to hit the busiest shopping period of the year.
Intriguingly, Bloomberg's report suggests two key things - that the new model will replace the current standard model (with the older iteration being phased out), and then be sold along with the Lite system. The report anticipates that the new model will have a price increase over the current $299USD, though Nintendo could arguably do this and pitch the Lite as the portable-only affordable option. As previously rumoured, Bloomberg's report claims the new system will be capable of 4K output when docked.