I do not believe there is sufficient evidence to confirm that the Aztecs could read Maya hieroglyphic writing. That is not to say because the Maya were no longer writing, but that their writing was much more restricted in the Postclassic. Rather than having texts featured on stela or monuments proclaiming the feats of a king, their genealogy, and major life events as the Maya liked to do in the Classic, by the Postclassic writing was restricted to murals within buildings, painted vessels that were often sent as gifts to other nobles, and in paper or deer skin codices. The use of the hieroglyphic system continued to the colonial period as evident in Friar Diego de Landa's writings. After his famous torching of Maya books, de Landa felt remorse years later and attempted to preserve what knowledge he could of their writing. Unfortunately with de Landa's limited understanding of other writing systems he was only able to create a list of sounds associated with some signs and did not record how words or sentences were formed. It wasn't until the 20th century that epigraphers made a breakthrough in understanding that the glyphs used in Maya writing were syllabic with parts of glyphs coming together to form words. Difficulties still lie today in understanding logograms, or glyphs made up of a unique symbol with little to no syllabic elements incorporated into their design. Without someone telling you what a logogram means or finding a text where a scribe wrote out phonetically what a logogram was, there is no real way of translating the glyph. Often these logograms are the names of people or places rather than verbs, other nouns, or other grammatical elements.

For the Aztecs, their interaction with the Maya region was largely indirect and distant. Between Central Mexico and the Maya region there were many physical, social, and political barriers to cross. That did not stop the Aztecs from conquering or controlling territory as they made their way east to the Maya region, most likely in the hopes of securing more stable and secure trade routes for goods like cacao, quetzal feathers, and other goods. Instead of using a hieroglyphic system of writing like the Maya, Zapotec, or Epi-Olmec, the Aztecs made use of pictographs in conjunction with artwork to act as mnemonic devices to recall already memorized knowledge or to create simple tributary lists from their territories. While Aztec art and writing could become very elaborate, their writing does not come close to being able to be read without outside context as Maya writing is able to be read.

But, who knows? Archaeologists are always finding new things. It is certainly possible, though unlikely, that there was someone in Central Mexico that could read Maya writing. It would be difficult to prove, even with Maya writing on murals or vessels, without other likelier explanations (such as importing a foreign artist for the murals or foreign vessels to gain prestige/power/capital).