Is it possible?
Yes. But in general, it will be less lucrative for inventor--a patent or application will generally give the inventor a upper hand in negotiations.
Is it likely to happen and/or likely to turn out as you want? Maybe, maybe not.
You can certainly sell things as you wish. There are some caveats in contract law about what selling something really means, and all that good stuff, but those aren't really covered by the scope of your question or this site.
The trouble with selling an unprotected invention, however, is two-fold:
- First, you don't have protection for it. You might be able to get away with an NDA, or some other form of contract that keeps the recipient company from stealing your invention and running with it, but nothing will protect you like a patent.
- Second, the company won't have protection for it. This is a little more serious. You can't NDA everyone, which means the company will be unprotected and other places will start popping up, selling your invention. That said, I can imagine a contract that involves the company funding a patent in lieu of some payment to you. Bear in mind, however, that such a deal would likely leave them in control of the patent, more than if they were simply licensing it from you.
Ultimately, there's a reason the patent system exists, and it's really difficult to get good protection for inventions whilst evading it.
In general, if you were to pursue such a path, you'd need to be extremely careful in dealings with any company looking to buy the unprotected invention, and indeed you likely wouldn't get as good of a deal as if you were the holder of a patent (or application).
I would heavily advise that you speak with a patent professional or at least go for provisional patent filing before making any moves, including, particularly since you mentioned international patents, talking to any potential customers of the invention rights. You might find that a provisional patent application is a more viable alternative to get started, or that professional may have experience in a similar case as yours.
You may be surprised to learn that filing a provisional patent application is not as expensive as you think. And with a lifetime of 12 months, such applications are a fantastic means of temporary protection while you work to struck a more promising deal.