You're focused on the stick. What's the carrot?

This guy is giving you a great opportunity to figure out what his job lacks for him. And, perhaps, what issues other people might have.

It could be that it's time for him to move on. Sometimes we all want a change of scenery, and your company may be too small to provide that for him. Or it could be that you kinda want him to go anyhow. In either of those cases, in your shoes I'd give him a firm date at which he is leaving. Whether or not he has his next job lined up by then is not your problem.

But if you want him to stay, then I would work hard to make your company a place he's excited to come to every day. He may not really know why he wants to leave; we developers are not generally very introspective. That means you may have to spend a fair bit of time with him figuring it out. But if you can come up with some options, then I'd offer those as the reason for staying, and forget entirely trying to find a stick.

I'll note that studies show that surveys of managers and developers show different motivators and priorities when choosing jobs, so the things that appeal to you may not work for him. You may need to check with other developers for ideas. And I'd also suggest that your joint reluctance to have him starting anything serious is a sign that you could improve your process by reducing grain size and shifting responsibility from individuals to teams. That will help you not just in this case, but with the engineers who aren't so open about their plans to leave.