Nope. You can only invite a villager from another town to move in, when they are in boxes.
- - - Post Merge - - -
Or where you talking about the 16 villager cycle? Once a villager moves out you have to move out another 16 villagers before you can invite the same villager to move back in, once you have cycled through enough they should no longer show up in your main street.
Once a villager moves out, you have to move out another 16 villagers before you can invite the same villager to move back in, once you have cycled through enough they should no longer show up in your main street.
Yeah, it's two full 8-villager cycles (hence 16). Eight is the normal max you can have to have a normal move in (normal meaning not counting SP, campsite, etc), so basically you have to have full-town turnover twice, which seems like a bit much, since most have certain favorites they don't want to see go, lowering the amount they're willing to lose, thus lengthening the time it takes to cycle through.