If you don't have an empty plot in your town, you won't be able to trigger the move in dialogue with a villager from someone else's town.
The most popular way of clearing a plot is to travel 15-30 days forwards and look for a villager with a thinking cloud. If the villager with the cloud is someone you want to keep, close the game without saving and TT one day forwards. Repeat until a villager you want to get rid of has the thinking cloud. Talk to them and let them leave. TT forwards 1 day (they will be in boxes), save and quit, TT 1 more day and their house will be gone.