The various extant and historically attested Mayan languages belong to the Mayan language family, while the various varieties of Nahuatl form a part of the larger Uto-Aztecan language family.

The Mayan and Uto-Aztecan languages have not been shown to the satisfaction of the linguistic community to share a common ancestor, so we have no evidence that they are related to one another.

That being said, both of these language groupings fall into the Mesoamerican language area, and share a number of common features likely due to long-term contact (Campbell et al. 1986). For instance, the languages in Mesoamerica have a specific possession construction, where for the equivalent of English the man's dog, you would find something like his-dog man. Additonally, while many surrounding languages have a word order of Subject-Object-Verb (compare English SVO She eats cake with Japanese SOV Kanojo-ga keiki-o taberu, literally 'She cake eats', and with Irish VSO Itheann sí císte, literally 'Eat-I cake'), there are no verb-final languages in the Mesoamerican language area.

So in the sense of having things in common for reasons other than sharing a common ancestor, they do certainly have things in common.