US President Donald Trump tweeted on Sunday that he had a "long and very good call" with his Chinese counterpart Xi Jinping and that a possible trade deal between the United States and China was progressing.
Risk appetite was strong going into the New York session. US stock futures are up nearly one percent.
On Monday, the dollar was down a quarter of a percent at 96.43, but it is set to close the year up more than 4.5 percent against its rivals.
The Australian dollar gained 0.4 percent to $0.7063 but on the year is down 10 percent.
China and the United States have been in a trade war for much of 2018, shaking world financial markets. The flow of hundreds of billions of dollars worth of goods between the world's two largest economies has been disrupted by tariffs.
Going into 2019, the outlook for the dollar is more subdued. Expectations are growing that a three-year cycle of rate increases in the United States is coming to a close.
Market expectations for no more rate hikes next year stand at nearly 80 percent compared to only a quarter a month-ago, according to the CME Fedwatch tool.
"Along with growing expectations of no more rate hikes, the familiar issues of the twin deficits is expected to weigh on the dollar next year," said Alvin Tan, a currency strategist at Societe Generale in London.
While the dollar has been relatively stable going into the end of 2018 despite falling US Treasury yields, concerns are growing over the dollar's outlook.
The US 10-year Treasury bond yield was at 2.71 percent on Monday, down nearly 30 basis points in December. Sterling has been battered this year by Brexit woes, but it rose to a three-week high in quiet trade. It rose more than half a percent against the dollar at $1.2765 but has lost more than 6 percent of its value versus the dollar this year.