Your question has nothing to do with the GPL. If your concern is that the code may count as derivative work of existing code then you also can't use that code in a proprietary way, under any license. But that probably only applies if the LLM regurgitated a substantial amount of copyrighted code into your codebase.
Fair; that was an example instance. People interested in “Free software” rather than “open source” seem to often favor the GPL, though other licensing options also count as “free software”.
But in any case, the question really refers to, can the LLM-generated software be copyrighted? If not, it can’t be put under any particular license.
Is your concern the potential for plagiarism or the lack of creative input from the human? If the latter, it would depend on how much intellectual input was needed from the human to steer the model, iterate on the solution etc.
If it can’t be copyrighted, then no. Licenses rely on the copyright holder’s right to grant the license. But that would also mean it’d be essentially public domain. I’m not sure there’s really settled legal opinion on this yet. Iirc it can’t be patented.
The way the world is currently working is code created by someone (using AI) is being dealt with as if it was authored by that someone. This is across companies and FOSS. I think it's going to settle with this pattern.
