I\'m simply wondering if it is possible to create a private network on Azure and place a web app there? I know I can put VM\'s, SQL instances etc, but my question concern We
Absolutely - you need to set up Virtual Network or Hybrid Connection:
Reference #1: Connect to on-premises SQL Server from a web app in Azure App Service using Hybrid Connections
Reference #2: Integrate your app with an Azure Virtual Network
Reference #3: How to place your Web App into the existing Virtual Network (your situation, i guess)
And you will have the VPN/Virtual Network that will give your solution the continuous IPs space.