UPDATE 2-Oil edges lower after gains driven by trade optimism

* Brent, WTI fall slightly

* Prices supported by trade hopes

Graphic on U.S. inventories: https://tmsnrt.rs/2XkQF8e (Adds latest on China-U.S. talks, updates prices)

By Aaron Sheldrick

TOKYO, Nov 5 (Reuters) - Oil prices steadied on Tuesday as investors kept an eye on U.S. inventory data due later in the day, following two days of gains on positive economic data and hopes for a Washington-Beijing trade deal.

Brent crude futures were down 1 cent at $62.12 a barrel at 0739 GMT after gaining 0.7% in the previous session.

U.S. crude futures were down 9 cents at $56.45 a barrel. They gained 0.6% on Monday.

"This is mostly position lightening after an impressive run higher," said Jeffrey Halley, senior market analyst at OANDA.

"Oil is vulnerable now to any sharp change in short-term investor sentiment," he said.

U.S. crude oil inventories were forecast to have risen last week, while refined products stocks likely declined, a preliminary Reuters poll showed on Monday.

Five analysts polled by Reuters estimated that crude inventories rose around 2.7 million barrels in the week to Nov. 1. Inventory data from the American Petroleum Institute is due out later on Tuesday, while official figures come out on Wednesday.

Oil has been supported by hopes for a trade deal between the United States and China, the world's two biggest oil users, that could boost demand.

China is pushing U.S. President Donald Trump to remove more tariffs imposed in September as part of a "phase one" U.S.-China trade deal, people familiar with the negotiations said on Monday.

The deal, which may be signed later this month by Trump and Chinese President Xi Jinping at a yet-to-be determined location, is expected to include a U.S. pledge to scrap planned tariffs on about $156 billion worth of Chinese imports, including cell phones, laptop computers and toys.

Oil investors are closely watching the initial public offering of Saudi Arabia's state oil company, Saudi Aramco, in what is expected to be the world's biggest listing.

Aramco's Chairman Yasser al-Rumayyan said on Sunday the state oil giant would continue to meet its global oil supply demand after it lists on the Riyadh bourse.

On the supply side, Russia cut its oil output <C-RU-OUT> to 11.23 million barrels per day (bpd) last month from 11.25 million bpd in September, but again missed its obligations under a pact to curb production.

The Organization of the Petroleum Exporting Countries (OPEC), Russia and other producers, a group known as OPEC+, have since January implemented a deal to cut oil output by 1.2 million barrels per day.

OPEC output rose in October from an eight-year low as a rapid recovery in Saudi Arabian production from attacks on oil plants more than offset losses in Ecuador and voluntary curbs under a supply pact, a Reuters survey found last week.

(Reporting by Aaron Sheldrick; editing by Richard Pullin and Christian Schmollinger)