Yes: medieval people expressly regarded themselves, the things they made, and their modes and styles as modern.

Modernus was a Late Latin coinage and was not used by classical authors such as Caesar, Cicero, Virgil, etc. The word was generated by turning the adverb modo which can have the meaning of "just now, presently" into an adjective to mean, well, "modern" as in "contemporary, happening now, not old."

We can date its appearance in writing to the late 5th century AD. In a 2006 article on the early use of modernus, John Moorhead observes that Augustine did not have this word when writing his Confessions around 400 even though it would have helped him. But it was certainly available to authors including Pope Gelasius I by 500. (I believe Gelasius provides the earliest examples.

A notable use is Cassiodorus' description in De Orthographia (ca. 580) of the grammarian Priscian (fl. 500) as an auctor modernus, "modern author," in contrast to others he discussed. Subsequently the term modernus was typically used to describe a person from the era of Christianity (what we would probably call "medieval"), in contrast to someone antiquus, basically the pagan past (what we would call "ancient" or "classical").

Besides individuals, durng what we call the Middle Ages a variety of things were described as modernus to indicate that they are the new or modern style. One of the names for what we call Gothic architecture was opus modernum, "modern work." Suger of St. Denis used this exact phrase. A style of preaching that started in the 13th century using scholastic methods of biblical interpretation was the sermo modernus, "modern sermon." In the late 14th century a new style of Christian religious practice originating in the Netherlands that emphasized individual prayer and meditation was called devotio moderna, "devotio moderna." Also by that time, scholastic philosophy was being called the via antiqua, "old way" whereas more the more recent philosophy of William of Ockham was the via moderna, "modern way."