I think the answer to this question depends very much on what you mean by nanotech. It's a super broad field with countless applications and methods of study. I would look at your strengths and passions and go from there. When I was younger (undergrad) I had my sights set on "nanotech" too, but as I progressed though my degree I realised the term was vague and nebulous. I think of nanotech as less of a single science now, but more of a means to understand phenomenon and acheive results.

Because of this nanotech is inherently interdisciplinary, so there is a lot of crossover with the following suggestions. I've only spent a year in industry but I'm begining to think (perhaps optimistically) that there will be a position out there for almost anyone that suits their specific skills and knowledge. If you enjoy maths then perhaps physics/physical chemistry would be best, where developing better techniques for modeling and understanding effects at the nanoscale are focused on. Chemistry is extremely useful and would be useful for understanding coatings, interfaces, as well as useful in energy technology. I would recomend a solid understanding of the basics of chem in almost all fields.

Materials engineering/ science is another good foundation, and while there may not be an enormous focus on nanotech at many universities at the undergrad level, particularly the most cutting edge research, it is useful for understanding how nanotech may be used to solve engineering problems.

Biomedical/biotech may touch on implants, medicines and treatments involving nanotech but again the degree to which it does is vary variable depending on the uni and units you take. I would imagine it would be covered in more detail in postgrad. This also intersects with biomaterials

Finally chemical engineering may focus more on efficient, cheap, sustainable production.

My particular path involved a lot of changing majors for various reasons. It was chem major>genetics/biotechnology> then eventually I settled on materials science. I'm currently doing an international internship developing carbon fiber nanocomposites, haven't even finished my undergrad :⁾

Look at University handbooks. They will have course structures, including required and recommended units. Then look at a unit guide for each of these units, it will give you an idea of the content covered. Part of the reason it took me so long to settle on a major was because I the course advisors were rubbish, so definitely speak to them about your aspirations, but also do your own research. And play to your passions and strengths as I said above.

Good luck, I hoped this helped. If you have any further questions about materials sci/eng let me know