I think I chose Rumors > General, at least 200 times now in Skyrim, and I haven't heard a single mention of the Oghma Infinium. And I am talking to an NPC that knows rumors, e.g. he doesn't keep saying, "ask someone else".

Does my character need to be a minimum level to get the quest?

Does your character already have an artefact ? You aren't given the opportunity to hunt down another unless genuinely losing the first, or you work your way around the limit by tucking it/them away for repairs for the time of the hunt.

The other problem (aside from already having an artifact) is that I heard that in each province, there is at least one artifact you cannot possibly get (with the exception of the Imperial Province, aka Cyrrodil). It could be that you cannot get the Infinium quest in Skyrim, so go to another province and try there.

If you are getting rumours about other artifacts, than that could be the problem. If you are getting no rumours about any artifacts, then you either already own one, or perhaps your level is too low and your Personality score too crappy.

Ogma Infinum will appear in Skyrim and Valenwood.

You will have to just keep asking just as Mr vampire said it appears in Skyrim and Morrowimd. I would suggest going to Morrowind good luck

If you're bound and determined to have a particular quest item, your best bet is to ALWAYS go to the Imperial City and ask around. As stated above, you can initiate the quest for ANY artifact therefrom. That way you don't waste time looking around in a province where the populace will never help you (at least, not in the way you want to be helped.)