Recently, a mysterious video was posted on Blizzard's official Twitter account, showing a Diablo-shaped lightswitch being turned on and off. Many interpreted this as a teaser for a Switch version of Diablo III, as this was literally a "Diablo switch". However, this is not the case.
In a response to the speculation given to Polygon Blizzard puts the rumour to rest:
"We can assure you we're not that clever. [It was] meant to be a fun community engagement piece. We have nothing to announce."
So, no Diablo III on Switch it seems? At least for now...