Scribbler noted: I do not know whether the gladiators always said, in a ritualistic fashion, exactly the same words, but the Latin phrase is usually quoted "Ave, Caesar! Morituri te salutamus!"

It is my understanding that "Morituri" is a future active participle, i.e. a verbal adjective which can therefore be used as a noun, as in the phrase "Morituri te salutant/salutamus" (I understand that it is used as a noun simply because there is no other nominal element for the subject position). In this case, "morituri" is a plural noun that could accompany any verb in the plural. So grammatically speaking, both "Morituri te salutant" and "Morituri te salutamus" are correct. If you were to add a pronoun to the sentence, such as "nos", "illi", that would certainly determine which verb form is adequate.

I have more often heard/read "Morituri te salutant" than "te salutamus", but this may be a fluke. Or maybe, as Scribbler notes, it was a fossilized, ritualistic phrase...