Now the world currency is the US dollar. If I'm not mistaken, there have already been attempts to create a single world currency - bitcoin. But while it is still not so popular and predictable as the dollar.
US dollar will still dominate the world currency even their would be more attempts to try replacing it, as they already show the world how powerful they are and they really wanted to control in any aspect even the new President got a lots of criticism but still US will not allow any possible thing to happen to removes their dollar as the world well known currency.
But America can't stop people using Bitcoin in all of the other countries in the world, and they don't even seem to feel threatened by Bitcoin, having a reasonably lenient stance to it, so I don't think they would be directly hostile.
I think also usa has nothing against bitcoin and that is a country which respects individual rights and wishes, they can live very well using dollar and bitcoins together. Each citizen will use the currency he wants and each store will accept the currency it wants.
Dollar will continue ruling the world for the nexr decades for sure. Bitcoin is weak yet to be accepted by the majority population parcel.