China had an immense hunger for silver, from all of its trading partners. There were several reasons for this. One was that silver was used as a store of value. After numerous depreciations in coin and paper, nobody trusted the government's currency, and there was never enough silver. Another was that silver wasn't subject to import duties! (The various import duties by themselves discount the notion that there was nothing the Chinese wanted to import...)
But the biggest reason to import silver to China is that China had a vastly different gold-to-silver exchange ratio than the rest of the world:
Chinese merchants did not simply pursue bullion; they sought one particular metal--- silver. The source of profit from silver was, of course, the high price silver commanded in China. The gold/silver ratio in China had drifted slightly downward from its historical peak of 1:4-5, achieved in the late fourteenth century, to 1:6 by the early sixteenth century. In contrast, the gold/silver ratio hovered around 1:2 in Europe, 1:10 in Persia, and 1:8 in India... --- Richard Von Glahn, "Fountain of Fortune: Money and Monetary Policy in China, 1000--1700", p. 127
Von Glahn argues that most of the silver imported into China actually came from Japan (once Japan opened significant silver mines), not the Americas. Some of this trade was carried out by Europeans, but by no means all.
I received "Fountain of Fortune" for Christmas and it's an interesting read. Much of it is about how the three conventional functions of money (store of value, measure of value, and unit of exchange) were served by different media for centuries. There are a variety of reasons for that--- one is that China simply couldn't mint enough bronze coin! A lot of Chinese bronze coin (like, entire shiploads) was imported into Japan for use there. But the perspective of the American bullion trade as merely a sideshow in a giant gold-silver arbitrage scheme is also an interesting bit of history to read too.