As I see it, this feature should be a report configuration property.
Currently, user could override ILogger in reporter configuration with his own instance that also prints logs to files, but it adds an additional complexity of usage. The easiest way to do it may be adding file provider to a logger if this property has been set.
Also, file template and file path should be customizable as well.
I would also consider refactoring reporter configuration in a fluent way to stick to one design approach. That means that configuration should be refactored to a method chain approach, as well as this new API.