
Windows Deployment Services (WDS) is the revised version of Remote Installation Services (RIS). WDS enables the deployment new clients with a network-based installation without requiring that administrators visit each computer or install directly from CD or DVD media. For how to set up and install WDS role, also on how to configure Windows Deployment Services on Windows Server 2019, and how to configure Windows Deployment Services on Windows Server 2019. For more information on WDS not referenced here, please visit the following link. In this article, you will learn how to fix the “No valid offer received: WDS PXE-E16 error when booting clients”.
When prompted with this error below, as I always say, there are many factors that can be responsible for this. Below is what I did to resolve my issue. Please see How to remove Windows Deployment Services role via the GUI and PowerShell, and how to fix WinRM cannot complete the operation, verify that the specified computer name is valid.

The solution to fixing no valid offer received: WDS PXE-E16 error when booting clients
Ensure the Windows Deployment Server Services are running. To verify this, logon to the WDS Server, and launch the Windows Deployment Services Tool.
Right-click on the server, select “All Tasks” and click on Start. Please see What are the differences between MDT and WDS?, and how to fix “The service could not be started either because it is disabled or because it has no enabled devices associated with it.“

The Windows Deployment Services have started successfully.

If the solution discussed above does not resolve your issue, kindly visit this link to see if what they discussed about this error can help you resolve your issue.
I hope you found this blog post helpful. If you have any questions, please let me know in the comment session.