Hamas accepted the draft agreement on the ceasefire in the Gaza Strip and the release of dozens of hostages. The Associated Press agency reported two unnamed officials participating in the negotiations.
Qatar, the mediator, said the talks had come to the "closest point" of agreeing.
An Israeli official said progress had been made, but details were still being worked out, and the plan must be submitted to Israel's cabinet for final approval.
Officials have expressed optimism that they will be able to sign an agreement on the eve of US President-elect Donald Trump's inauguration, which is scheduled for January 20.
