Ziyad Abu Ziyad, of East Jerusalem, said Mr Arafat announced the dates during a briefing on talks he had held with Israel on the Hebron deal.
"If the Israelis go ahead with their promises and the plans which were planned, maybe it will be possible to conclude an agreement on the 30th and the 31st [of December]," he said.
The remarks supported the forecast of a senior Israeli official on Tuesday that there would be a deal by the end of the year. A summit that day between Mr Arafat and Benjamin Netanyahu, Israeli Prime Minister, ended weeks of deadlock in talks on Israel's hand-over of 80 per cent of Hebron to the Palestinians in the Israeli-occupied West Bank. Tensions remain high in Hebron. A petrol bomb was thrown near the town's Jewish enclave but caused no injuries or damage.
Most of Mr Netanyahu's cabinet are expected to back the deal though some say it spells danger for Jews in Hebron.
The US Middle East envoy Dennis Ross headed home to brief President Bill Clinton on the talks. He said he would be back on Monday to seal the agreement.