I suspect the question might relate to the Meraki platform itself, in which case: no - you can’t host a ‘private Meraki Dashboard’ anywhere (in private DC or public cloud platform). One of the primary benefits of the Meraki solution, for most customers, is that they don’t have to do anything to build and maintain the underlying platform themselves - Meraki does this privately.
What’s the reason for wanting to host it yourself (albeit in the cloud)?