You might be interested in a previous answer of mine that addresses a similar question, it emerged as a clarification on the difference between the "Mexica", the dominant group of the Triple Allaicne, commonly known as the Aztec Empire and the "Aztecs" and other "Nahwa" groups, or on u/jabberwockxeno 's answer that the initial comment links to:
I dont know if this is what you're asking for but to this day there are noble houses, especially spanish that can track their ancestry to the Aztecs like the House of Moctezuma, if you're asking for individuals who might be interested in doing so, well obviously the indigenous groups that currently exist in Mexico are often able to do so (as a matter of pride as much as a matter of practicality and legal protection), for anyone else, that might be harder.
While there are colonial authors like Domingo de Chimalpain who make efforts to legally trace back their ancestry (and more importantly that of his community) to pre-hispanic times, and in fact a great source of information exists in the form of legal claims by native communities to land or other rights addresed to the colonial spanish government, many of them still exist as cultural artifacts or as part of the National Archive in Mexico City, otherwise most documents of that nature if they existed in pre-hispanic times were largely destroyed during the conquest and subsequent colonial periods, so I would find it difficult, though perhaps not as completely impossible as it would appear at first glance.