Details about the adjournment and resumption of negotiations were still being worked out, though the source said on condition of anonymity that Iran could not expect any new sanctions relief for the time being, Reuters reports.
Possible venues include Vienna and Oman, the source said, though nothing had been decided.
"Some progress has been made," said a diplomat involved in the talks. "But we need to discuss some issues with our capitals. We will meet again before the New Year. This is an ongoing process.
A European official said the possibility of securing a final agreement "seems physically impossible".
However, Iran's official IRNA news agency on Monday quoted a source close to the Iranian negotiating team as saying they were still focused on reaching an agreement.
With the deadline just hours away, a possible extension was one of several options for negotiations raised when U.S. Secretary of State John Kerry met Iranian Foreign Minister Mohammad Javad Zarif on Sunday, a senior U.S. official said on condition of anonymity.
Meanwhile Iranian foreign Minister Mohammad Javad Zarif and US Secretary of State John Kerry held their second bilateral meeting on Monday on the seventh day of the 10th round of nuclear talks.
A source close to the Iranian negotiating team said on Sunday after Zarif-Kerry 75-minite talks that the two discussed various scenarios including ways to continue nuclear talks, IRNA reported.
The two foreign ministers have also held five trilateral meetings with the EU nuclear coordinator Catherine Ashton since the beginning of the ongoing nuclear talks in Vienna on November 18.
Later on the day Iranian Foreign Minister Mohammad Javad Zarif conferred latest developments regarding the nuclear issue with his Chinese counterpart and EU coordinator.
Zarif started the seventh day of nuclear talks with a meeting with Chinese Foreign Minister Wang Yi.
Later on, Zarif discussed the issues of mutual interest with EU nuclear coordinator Catherine Ashton.
The G5+1 top negotiators will have a meeting in the coming hours during which they will make the final decision.
November 24 is set as the deadline for Iran-G5+1 nuclear talks. The Iranian negotiating team said there would be no extension for the talks as the two sides have to focus on reaching a comprehensive agreement to end the decades-long nuclear dispute.