I'm a tech writer here at Splunk and I'd like to help. It looks like search managers manage inline searches, but according to this documentation, SavedSearchManagers can handle a search saved as a report:
There are also post-process search managers available. This documentation resource offers details on the different kinds of search managers:
This Simple XML reference also details referring to a search saved as a report within the Simple XML search element:
I hope this helps! Please let me know either way and we can continue discussing.
All the best,