The closest they've come to a direct connection (aside from quoting Bear McCreary's Constantine theme music in John's first couple of Arrowverse appearances, and putting John in what I'm pretty sure is the same trenchcoat) was last season -- when Mallus impersonated the voice of Astra Logue (the girl that Constantine inadvertently got damned to hell in the formative Newcastle incident), they got the same actress, Bailey Tippen, who played Astra in the NBC series.
They also indirectly alluded to it in the season premiere, when Constantine came to Sara and said "The darkness -- it's rising." Though he turned out not to be referring to the same "Rising Darkness" that was the threat in the NBC show.