As Logic Apps is a multi-tenant PaaS offering, there isn’t a server instance dedicated to you that you can host or connect to your own VNET. You do have multiple options for network connectivity of Logic Apps:
- Use Azure API Management as it can be configured to work across VNET.
- Proxy the calls from Logic Apps to an on-premises service via a API/Web App or Function. The API/Web App or Azure Function comes with an App Service plan which lets you associate it with a VNET.
- Leverage the PowerBI On-premises data gateway for a number of popular services – file, SQL, SAP, Oracle, MySQL.
Related to this topic you may want to read Microsoft’s IT Showcase “Redesigning network topology for modern app architecture”.