Cloud Run on Anthos GKE

I deployed a service on Cloud Run on Anthos GKE cluster with internal only VPC access. This service should not be exposed externally to the public. 
 
Deployment was successful. But the domain name mapping for the service is by default providing the GKE cluster external IP. This kind of beats the purpose of deploying the service on Anthos to limit the access to internal VPC.
 
I did some workaround by creating a Cloud DNS with private zone and created record with Cloud Run mapping of the subdomain and assigned the GKE internal IP for the service. 
 
In the cloud run, the service is mapped to the domain mapping but with the external IP. The domain validation fails as there are no external DNS record updated for the subdomain. However, I can now access the service through internal VPC components. Is there a way for the cloud run to do a domain resolution using cloud DNS mapping rather than an external domain name? 
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Have you tried setting up the internal network as described in this document

https://cloud.google.com/anthos/run/docs/setup#setting_up_a_private_internal_network

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