I think she would look up to him, at the very least. Might ask him questions about whether she chose the right career path and whatnot.
Knowing that Oliver played with Ginny for Gryffindor, I can definitely see him being worried about her during that time. Her marriage was NOT good for the first couple years, and she definitely took it out on the pitch. Things have improved greatly over the years, and I feel given her position with the Prophet, him coaching Travis, and so on, they might be very good friends.
Lily wouldn't have wanted serious either, though she does go all mushy around babies, so if that didn't scare him off, it probably would've fallen apart on its own. She loves attention and praise, so while she may not be actively 'flirting' with everyone, sometimes it can come off like that.