No not really. "AIs" today are entirely digital LLMs that can be copied, shared and redistributed for a marginal fee already. "Collecting" AI would make absolutely no sense, especially since most of the AIs worth collecting cannot be used for commercial/museum-fee purposes. The only such thing that will exist in the future are the people that digitally archive today's model files.
Music can be copied, shared and redistributed for a marginal fee. Text even more. Nevertheless, you have record and book collectors. What's the difference?
In that case, they can collect whatever they want. The unique or special value of owning it in your collection is effectively nothing since I can enjoy the full-fidelity version at no cost wherever I go. This is the inherent problem with "collecting" something that is digital and can be infinitely reproduced.
I collect things because they're unique. Things that exist everywhere in abundance are not interesting to me. I could collect Coke-a-Cola bottles, but that wouldn't be special; I'd just be hoarding a bunch of trash.
I collect them using ollama. My favorite go to is nous-hermes2-mixtral, though others have things to say. They're all distinctive (phi3, llama3, wizardly, etc.) and can be a riot with the right prompts.