Okay, I'm still noodling this one but for now this is what I got...
Jesus
Muhammad
Buddha (Siddhartha Gautama)
Adolf Hitler
Genghis Khan
Confucius
Nelson Mandela
Mao Zedong
Mahatma Ghandi
Alexander the Great
The first 5 I'm pretty sure about. The second 5 make my list for now but they're close enough calls that I'm considering replacing them, possibly with someone from my list of the last 5 to miss the cut...
Marco Polo
Michael Jackson
Muhammad Ali
Mother Teresa
Julius Caesar
There are as well a few others that I can't quite rule out yet. Given how much of the world's population lives in Asia, the most viable candidates are those that have some nexus that would create strong awareness of them in both the Eastern and Western Worlds. And to some extent recent significance helps. I doubt that 500 years from now Nelson Mandela or Mahatma Ghandi would make the list. But at the same time, recent fame has a hard time overcoming the broad awareness (in both the Eastern and Western Worlds) that lasting historic significance creates. That's why I don't think, e.g., Michael Jackson or Muhammad Ali quite make the top 10. Also, I think being one of a group that might be brought to mind in similar contexts hurts potential candidates individually. I'm thinking, e.g., of: Aristotle, Plato, and Socrates; Elizabeth I, Henry VIII, and Elizabeth II; Mozart, Beethoven, and Bach; Lincoln, Washington, and Franklin. No doubt British monarchs taken together deserve at least one spot in such a top 10, but which one on their own would?
Napoleon Bonaparte was the last to come off my last to miss the cut list. I feel like he should be in there somehow, but I don't see why he'd be as recognized throughout Asia as some of the others.