Some of my other villagers have been talking about Limberg leaving (finally!), but when I talked to him he didn't mention it :/ . When is he going to ping me to move?
Or just don't talk to him. He'll move in 5 days, you don't have to tell him to or not. I often do this with villagers I want out. I don't talk to them at all and they'll be in boxes in 5 days.
Tifany's right. If he never pings you about it, it's okay. He'll skedaddle in a few days regardless and be like "Oh, I forgot to tell you I'm moving out."