Approaching unresponsive high level research professor as an undergraduate without any program
Well, faculty-student research is a two-way street, and for whatever reason, it certainly doesn't sound like this professor is showing a lot of interest in working with you.  This is not necessarily anything about you or your abilities; he may just be busy with other things, or not very interested in working with undergraduates in general, or too disorganized to keep track of potential research students.  But any of those would suggest that this is not someone that would be a good research supervisor for you at this time.

If you did start a research project with this professor, you'd be counting on him for actual supervision: advice on what to learn and what to work on, feedback on your progress and on your products (papers, code, etc), availability to meet to help get you unstuck when you are stuck on a problem, signing necessary university paperwork, collaboration in writing and submitting papers if you get that far, and so on.  You can see from many questions on this site how frustrating a research experience can be if this sort of support is not forthcoming, and it will be especially important in your case since it's apparently your first time getting involved in research.   And the fact that he is already so unresponsive to something as simple as "I'd like to talk about research opportunities" is reason for serious concern that he'd be similarly unresponsive when you really need his participation.

I would suggest that, at least for now, you move on and look for research opportunities with other faculty members - ideally, someone with a record of working successfully with undergraduates, and who shows clear interest in working with you.  I think these are more important than a perfect fit of research interests.

You have plenty of time to consider approaching this professor again in a year or two.  In the meantime, you might try to talk to other students he's supervised (either undergraduate or graduate) and find out how the experience was.  This may give you some ideas about how to get his attention more effectively, or it may convince you that you don't want to work with him at all.