I also like KiCad, but never used Verilog and do not know what such a program should do.
As KiCad is fully Free & Open Source software there are a lot of "side projects" around KiCad. From extracting component data from PDF's. scripts for generating netlists, tools for generating different kind of BOM lists and many more.
Some are well maintained, others are in varying levels of bitrot.
I've seen pages on github where some people kept lists of such tools of external projects around KiCad.
File formats in KiCad are also Open and pretty easily readable ASCII, and tools / libaries for writing those files are of course also a part of the KiCad project.
But what sort of level of conversion are you looking for?
Just a netlist thing, or do you want it to automatically insert a softcore if you use a uC in your schematic?