Yes, you could use a private registry---Docker Trusted Registry for Azure Container Instance.
Containers are built from images that are stored in one or more
repositories. These repositories can belong to a public registry, like
Docker Hub, or to a private registry. An example of a private registry
is the Docker Trusted Registry, which can be installed on-premises or
in a virtual private cloud. You can also use cloud-based private
container registry services, including Azure Container Registry.
A publicly available container image does not guarantee security.
Container images consist of multiple software layers, and each
software layer might have vulnerabilities. To help reduce the threat
of attacks, you should store and retrieve images from a private
registry, such as Azure Container Registry or Docker Trusted Registry.
In addition to providing a managed private registry, Azure Container
Registry supports service principal-based authentication through Azure
Active Directory for basic authentication flows. This authentication
includes role-based access for read-only (pull), write (push), and
other permissions.
When you create the ACI via the Azure portal, you will see the three options.
