If you're not time traveling at all, you basically have to just ignore them, and hope they eventually get the move out thought bubble. In the same sense, if you're not time traveling, and you see the thought bubble on some villagers head that you don't want them to move out, don't talk to them. If you do, it resets the thought bubble "move out" time, and it will take another week or two for it to come again.
If you aren't opposed to time traveling, an easy method is: Day 1, talk to a couple of villagers, then save your game. Time travel 1 month in advance, and make sure it isn't a Saturday (villagers can't want to move out when KK is there). Look for the thought bubble. If it's not on the desired villager, save / close the game, and TT +1 day ahead (don't talk to the villager if it's not the one you want to move out). Repeat until you get the thought bubble on the desired villager.