Did the ancient Greeks and Romans have the idea (at least partly) similar to the concept the Proto-Indoeuropean language?

Many among the elite spoke Greek fluently or at least learnt it intensively. There were close contacts with the speakers of the other IE languages like Gallic, German ancestor, Parthian, even Indian languages (trade and wars with India as early as Alexander the Great). Besides, the languages were less divergent from PIE 2-3 thousand years ago.

Did someone come up with the idea about the intrinsic connection between the IE languages (or at least Greek and Latin)?

If not, why would it be hard to come up with back then?

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    Romans who thought about it recognised that there were similarities in the grammar and vocabulary between Greek and Latin. I'm not aware of any speculations further afield; and I don't think the idea of a proto-language appeared before William Jones' work in the 1780s
    – Colin Fine
    Commented Feb 10, 2020 at 22:47