There will never be one currency for the whole world. This world will never be one, we're all individuals and we want to live in our own country, with our own currency. So, the world will always be divided in separate countries. If you look at Europe and the Euro, it's almost falling apart.
The only thing that could work is one cryptocurrency next to all the fiat currencies of each country. This could be Bitcoin or any other cryptocurrency that can handle all transactions.
If this currency doesn't belong to just one country or only to a small group of people, I don't see any reason why it won't be used everywhere if it proves itself useful and efficient. We already use the same Internet and live in the same informational space. So why can't there be a universal currency?
This is what we should expect if there are no economic and informational barriers between people in the world.