In a perfect world, you'd have the report logic encapsulated in an abap class or a dedicated function module and use that as the basis for both your report and the RFC calls. But if this is a standard SAP report and SAP themselves weren't nice enough to provide said function module, you may not have this option.
I don't think this is the best solution for your request, but just to add another option to the ones already mentioned in other answers: the commercial product Theobald Xtract Universal can execute reports and return the results using several available destination types. Xtract is a windows service that offers connectivity to several target database types as well as a http based result stream. It isn't cheap though, and it essentially only can connect to SAP Netweaver based systems as its data source (at least S/4 is already supported). Target destinations have to be purchased extra, but at least not per system, only per destination type (Oracle, MySQL, MSSQL...).
https://theobald-software.com/en/xtract-universal/
Xtract Universal uses a number of customer function modules to execute the report in the target system, catch the output and return it, essentially as a wall of text. You'll have to parse that result yourself, you won't get a nice pre-parsed table with data in it.
Just to make sure there's no misunderstanding about a possible conflict of interest: I don't work for Theobald, but we are a paying customer and use Xtract for our own data extractions. It is very simple to use, can be executed in scripts, but as said, just does that one job.