UPDATE 6-Oil rises after Russia leans towards output cut

* Russia accepts need for cuts, bargains with Saudi - sources

* Optimism on trade talks ahead of G20 meeting

* U.S. inventories rise for tenth straight week

* U.S. crude reserves hit record highs in 2017 -EIA (Updates prices, adds U.S. stockpile estimate; changes dateline, previous London)

NEW YORK, Nov 29 (Reuters) - Oil reversed course and rose as much as 3 percent on Thursday, after industry sources said Russia had accepted the need to cut production, together with OPEC ahead of its meeting next week.

Prices, however, were still set for its biggest one-month fall in November since the depths of the financial crisis in 2008, having lost about 22 percent so far.

A seemingly relentless rise in crude supply from the United States, now the world's top producer, together with Saudi Arabia's insistence that it will not cut output on its own to stabilize the market, earlier sent Brent crude to another 2018 low below $58 a barrel.

Prices rebounded after sources said Russia would consider join an effort to cut alongside Saudi Arabia and other members of the Organization of the Petroleum Exporting Countries.

The Russian Energy Ministry held a meeting with the heads of domestic oil producers on Tuesday, before a gathering in Vienna of OPEC and its allies on Dec. 6-7.

"The idea at the meeting was that Russia needs to reduce. The key question is how quickly and by how much," said one source familiar with the talks between Russian oil firms and the ministry.

The market now expects that a cut of 1 million barrels per day would be possible from OPEC and its allies, said John Kilduff, partner at Again Capital in New York.

Brent crude futures traded up $1.24, or 2.1 percent, at $60.02 a barrel by 11:43 a.m. EST (1643 GMT), off an earlier session low of $57.50. U.S. crude futures rose $1.64, or 3.3 percent, to $51.94 a barrel.

Russian President Vladimir Putin, whose country is the world's second biggest oil producer, said on Wednesday he was in touch with OPEC and ready to continue cooperation on supply if needed, but he was satisfied with an oil price of $60.

U.S. crude inventories hit their highest in a year, and are now only 80 million barrels below March 2017's record 535 million barrels, according to the Energy Information Administration.

U.S. stockpiles were expected to build again in the latest week, traders said, citing data from energy information service Genscape. Crude stockpiles at the Cushing, Oklahoma hub rose 771,924 barrels since Nov. 23, traders said on Thursday, citing a weekly Genscape report.

U.S. oil reserves in 2017 exceeded a 47-year-old record when they increased 6.4 billion barrels, or 19.5 percent, to 39.2 billion barrels, the government said.

Investors in commodity markets are looking ahead to the meeting of leaders of the Group of 20 nations (G20), the world's biggest economies, on Nov. 30 and Dec. 1, with the U.S.-China trade war a key focus.

"We have seen huge increases in supply and the demand picture is in question. However, we might see some movement on global trade issues at the G20 meeting which starts on Friday," said Michael McCarthy, chief strategist at CMC Markets and Stockbroking.

Anticipation of the meeting may also be driving prices higher, said Kilduff of Again Capital, adding that traders are wary of being short ahead of the meeting. (Additional reporting by Amanda Cooper in London, Jane Chung in SEOUL and Naveen Thukral in SINGAPORE; Editing by Marguerita Choy and Kirsten Donovan)