I had a similar issue myself recently. Try this.
Open Tools-Distribution-OS Provisioning
Click the icon that looks like three people to open Public variables.
Check the variable "corename" and make sure it has the name of the core correctly entered. Now for the part where mine was broken.
Open Tools-Distribution-Content replication
Click on Preferred servers (Targets)
Make sure you have an entry in here for the core and that the server name perfectly matches the entry for the "corename" public variable.
Test the Read-only credentials for the core entry and verify that it is successful. (NOTE: no sources need to be configured for the core, it is not really a preferred server but it uses this to get the read credentials)
My issue was that the preferred server entry for my core was FQDN and my public variable was not. The name has to match perfectly.