EU officials were cited by Bloomberg as saying that there could be a breakthrough before the end of Tuesday.
The dollar index, which measures the greenback against six major peers, decreased 0.16 percent at 98.2867 in late trading.
In late New York trading, the euro was up to 1.1034 U.S. dollars from 1.1031 dollars in the previous session, and the British pound increased to 1.2781 dollars from 1.2576 dollars in the previous session. The Australian dollar was down to 0.6752 dollar from 0.6774 dollar.
The dollar bought 108.84 Japanese yen, higher than 108.35 Japanese yen of the previous session. The dollar increased to 0.9986 Swiss franc from 0.9969 Swiss franc, and it fell to 1.3203 Canadian dollars from 1.3230 Canadian dollars.