* U.S. officials hear rebel rejection of Russian idea

* Army source estimates operation will be finished in weeks

* Syrian army and allies advance deeper into rebel enclave

* U.N. Security Council to vote on ceasefire on Monday

* People who fled rebel areas return to see homes

* Tens of thousands estimated in shrinking rebel enclave

(Recasts with latest advances)

By Tom Perry

BEIRUT, Dec 4 (Reuters) - The Syrian army and allied militia advanced towards rebel-held areas of Aleppo's Old City on Sunday, thrusting deeper into opposition parts of the city in a relentless attack which a military source said would be over in a matter of weeks.

A senior rebel official told Reuters rebel groups in Aleppo had told the United States they will not leave their besieged, shrinking enclave, responding to Russian call for talks with Washington over their withdrawal.

But facing relentless bombardment and ground assaults, the rebels may eventually have no choice but to negotiate a withdrawal from eastern Aleppo, where tens of thousands of civilians are thought to be sheltering.

The Western and regional states that have backed the rebellion appear unwilling or unable to do anything to prevent a major defeat for the opposition fighting to topple President Bashar al-Assad, whose campaign to regain all Aleppo has been backed by the Russian air force and Iranian-sponsored militias.

The army announced new advances, which were confirmed by a rebel official with the Jabha Shamiya group. The advancing forces may soon reach a strategically important eye hospital, the capture of which would threaten further gains near the Old City, the official said, speaking to Reuters from Turkey.

Loud explosions were heard coming from eastern Aleppo as night fell, Reuters journalists in the government-held part of the city said. The Jabha Shamiya official said further advances may force a rebel withdrawal to the southwestern corner of their enclave. "The areas of Old Aleppo will be threatened to a great degree," said the official. "It is scorched earth."

The U.N. Security Council is due to vote on Monday on a draft resolution that would demand an initial seven-day truce in Aleppo, which could then be renewed. But it was unclear if veto-power Moscow would block the resolution.

Restoring full control over Aleppo would mark the biggest triumph yet for Assad in a war that spiralled from protests against his rule in 2011. The campaign waged by the Syrian army and its allies in Aleppo is one of the most ferocious of the war, with hundreds reported killed in recent weeks alone.

Russia said on Saturday it was ready for talks with the United States over a full withdrawal of rebels from Aleppo.

Speaking to Reuters from Turkey, senior rebel official Zakaria Malahifji of the Fastaqim group said rebels fighting in Aleppo told U.S. officials on Saturday they would not leave the city.

"Our response to the Americans was as follows: 'we cannot leave our city, our homes, to the mercenary militias that the regime has mobilised in Aleppo'," said Malahifji.

"They listened to the response and did not comment," he said, adding the rebel groups had reiterated calls for humanitarian corridors to be opened for the delivery of food and medicine into eastern Aleppo and the evacuation of the wounded.

The United States has yet to comment on the proposal made by Russian Foreign Minister Sergei Lavrov for talks on the withdrawal of all rebel fighters "without exclusion" from Aleppo. urn:newsml:reuters.com:*:nL5N1DY08A

ARMY EXPECTS TO TAKE EASTERN ALEPPO "IN WEEKS"

The rebels said the Russians had retreated from proposals agreed at talks with rebel groups in Turkey that would have resulted in jihadist fighters leaving the city, a ceasefire and humanitarian aid deliveries.

The Syrian army has vowed to crush the rebels in Aleppo.

"The expectation is weeks," the military source said, referring to the timeframe for taking back the whole city.

"The Syrian Arab Army will continue to implement its missions until the elimination of the terrorists and the recovery of control over all the eastern districts," he said.

The United Nations estimates that close to 30,000 people have been displaced by the latest fighting, 18,000 of them leaving to government-held areas, a further 8,500 going to the Kurdish-controlled neighbourhood of Sheikh Maqsoud and the rest moving within rebel-held areas.

U.N. envoy Staffan de Mistura has said more than 100,000 people may still be in the rebel-held area. The Syrian Observatory for Human Rights, a Britain-based group that reports on the war, said it could be as many as 200,000 people.

Food and fuel supplies are critically low in eastern Aleppo, where hospitals have been repeatedly bombed out of operation.

The rebels, including foreign-backed groups, say they have been abandoned to their fate in a war against better armed enemies including the highly trained Lebanese group Hezbollah.

PEOPLE INSPECT HOMES

In another blow to the rebels, the head of a new rebel alliance in Aleppo, "The Aleppo Army", was seriously wounded on Saturday, the rebel officials said.

The Syrian Observatory for Human Rights said the army or its allies were attacking in at least eight places in effort to deplete their ammunition and manpower.

Observatory Director Rami Abdulrahman said the pro-government forces were seeking to drive another wedge into the rebel-held sector from Aleppo's ancient citadel southwards.

Residents who fled eastern Aleppo for government-held areas early in the war began returning to the Hanano district recently captured from the rebels to inspect their homes.

The government took journalists to the district of northeastern Aleppo on Sunday, using a road through the city centre that was reopened two days ago.

A Reuters journalist said buses leaving from western Aleppo were bringing a steady stream of people to inspect homes they had not seen in years. Russian military trucks also delivered aid to the captured eastern districts of eastern Aleppo.

(Additional reporting by Firas Makdesi in Aleppo and Michelle Nichols in New York, and Suleiman al-Khalidi in Amman; Writing by Tom Perry; Editing by Janet Lawrence and Clelia Oziel) ((thomas.perry@thomsonreuters.com; Reuters Messaging: thomas.perry.reuters.com@reuters.net))

Keywords: MIDEAST CRISIS/SYRIA REBELS