You seem to be asking when an outpost is incorporated within a city's walls, becoming part of that city and not something you can select separately. If that is what you are asking, then it should become incorporated when there is a completed city structure adjacent to the outpost. Same applies to world resources like shards. I personally would not recommend having outposts close enough to cities that you can incorporate them into the settlement, unless you needed it to grab an extra piece of territory before an AI could claim it, or something like that.

On the other hand, if by "connected" you mean they have the little dotted line going to a city, then that goes to the closest city, although I don't know how tie-breaking works, and I don't know if it goes to the closest city hub or the closest city tile.