My adviser is leaving. Can I ask him to support my application for an other PhD position?
Your advisor has offered three options. You have a fourth. My best guess is that the advisor just forgot that fourth option rather than considered and rejected it. 

I strongly suggest that you ask him for your support in starting over at a different university. Any ethical advisor should support you. If you've been doing good work, they should support you strongly. 

In your request, though, I'd do two things. The first is to talk about the research trajectory that you would like to get on and suggest a few places (and even professors) where it would be possible. The second is to ask, also, for his suggestions about places to pursue your goals. He may well have contacts that can be useful to you in changing. Try to make your change a cooperative endeavor with the professor, not a break. The future may hold collaborative opportunities if you work it right.