Yes. Flat-field correction is the appropriate method for this kind of radial brightness falloff, even if the cause is lighting rather than the lens itself.

To use it, capture a reference “flat field” with the same camera/lens setup. Photograph a plain white surface that is evenly illuminated and slightly out of focus. The goal is to record only the illumination pattern and falloff, not scene detail.

You do not need a photo of the same background with the subject removed. Instead, you need a uniform reference frame made under the same setup so the software can measure and compensate for the uneven brightness across the image.

If your editor supports flat-field correction, that reference image can then be used to normalize the brightness in your real photos.