A lot of people seem to think that Nintendo have to fork Android, that really isnt true.
Historically per unit fees for mobile to Google are $5-$15 per unit based on volume and suite of applications. Basic Android is free (which by itself would be fine for a games console) but Google charge for running their apps on top of it - Gmail, Youtube, Maps etc.
Since its a game console with its own interface, its not necessary for it to have games on Google Play - it can just have its own app store. Nintendo may prefer that anyway, eg they may not WANT the comments and reviews that are visible to google play apps.
Also, Google like to work with external partners. For example they dont have any VR solution apart from cardboard - so that right there could be a focus for Nintendo. That would be an amazing fit since the biggest (not necessarily best but biggest) source of VR compatible video content may end up being Youtube since they announced they are making VR/cardboard a supported video type on youtube. They announced at Google IO that they have 1 million cardboard viewers.