Yes, this is possible. However you will need to use Private Endpoint. The summary is below
- Create a Private Endpoint for the Azure Cache for Redis in one of the VNets. See, to create a PE. Create a private endpoint with a new Azure Cache for Redis instance
- Set up VNet peering between the three VNets. https://learn.microsoft.com/en-us/azure/virtual-network/tutorial-connect-virtual-networks-portal
- Configure DNS resolution for the Private Endpoint.
- Update the App Services to use the private connection. https://learn.microsoft.com/en-us/azure/app-service/overview-vnet-integration
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Regards,
Abiola