In an interview with Sky News, Juncker said that "we can have a deal" and he believed "Brexit will happen."
He added that a no-deal Brexit would be "catastrophic" and he was doing "everything to get a deal."
The dollar index, which measures the greenback against six major peers, was down 0.30 percent at 98.2768 in late trading.
In late New York trading, the euro rose to 1.1053 dollars from 1.1031 dollars in the previous session, and the British pound was up to 1.2536 dollars from 1.2463 U.S. dollars in the previous session. The Australian dollar decreased to 0.6799 dollar from 0.6824 dollar.
The U.S. dollar bought 107.98 Japanese yen, lower than 108.35 Japanese yen of the previous session. The U.S. dollar decreased to 0.9919 Swiss franc from 0.9971 Swiss franc, and it fell to 1.3256 Canadian dollars from 1.3295 Canadian dollars.