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.
If bitcoin is really dangerous that could destroy the US's economy then there's still possibility that the US will force other countries to ban bitcoin. See what's happening to those countries with damn tonnes of oil which are now "touched" by the US? Everything is possible in this world. Not going to judge what US have done but they're really want to hold on the top position of superpower country.