Often when someone says his dog is untrainable he means there is a specific problem that has become unmanageable by jumping on people despite all kinds of perceived punishment or when a dog is slow to house train. Another meaning for the training failure is a dog who is difficult to motivate. If you can't find anything your dog wants from you, it could be hard to get him to do anything that you want him to do. But training is just another name for learning. Individuals who can't learn, don't stay alive for long. So if a dog is alive, he is trainable.
What motivators have you tried? It's possible there is nothing your dog likes. Nothing. Not food, not a toy, not tug of war, not going outside and not getting inside. If that's the case, he likes staying still. So make him work to be able to stay still. I think you see my point. There is something he does by choice and getting him to do what you want in order to have that choice is a motivation scheme.
What behavior is causing trouble? I want you to answer both which behavior your dog exhibits that you don't like and which one you trigger it or reinforce it with. Because if your dog is doing something that you don't like, then you are not preventing it or your reaction (no matter what it is) is actually rewarding or having no effect at all. Stop doing that.
If the behavior once you change what you were doing, then the behavior itself must be rewarding to do - to your dog. Your task is to make it less rewarding or make it actually uncomfortable-for your dog. Dogs don't mind being pushed or yelled at for jumping. Remember, I said stop doing that. So what is it about jumping that he likes? Reaching you? Greeting you? Make it possible to do those things another way. Stoop down or target train him to touch your hand instead. Still "un trainable"?
Place a leash on your dog and tether him to a door. Take a step toward him. If his feet come off the floor, retreat so he can't touch you. If his feet stay down, touch him and quickly get out of range again. Do this about 5 times. Quit for now and try it again two more times the same day. Skip a day. Try three trials again on day three. This time he's probably aware that if his feet stay on the ground, you will pet him. If they don't you won't.
Does he stay on the ground? Then he likes you to pet him. If he does NOT stop jumping, then he does not like petting enough to overcome wanting to jump. Choose tossing a bit of meat instead. Feet on the floor = meat. Feet off the floor = no meat. He doesn't like meat? Try opening the door to let him out or in (whichever he likes most). Once he usually keeps his feet on the floor while you approach, start saying "Off" when you approach and gradually relax your use of the tether (step on the leash if you need to) and then gradually wean yourselves off the leash. Practice in trying circumstances until he can almost always resist jumping on you when you say off. Now try it with someone new, from the beginning if necessary.
So you see the point. If problem behavior persists, change what you do to cause or correct it. If it still persists, make it impossible or unrewarding. If the behavior is still occurring, teach an opposing behavior and practice in distracting circumstances until your problem is solved.
The most common comments I hear after giving this advice are first, "I can't believe how fast it worked. It only took a week then we practiced another week" and second, "We didn't try it". Remember the best time to start training your dog is last month. The second best time is today.