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UPDATE 1-White House adviser holds out hope for progress in U.S.-China trade talks

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WASHINGTON, Oct 4 (Reuters) - White House economic adviser Larry Kudlow held out hope on Friday for progress in opening China's financial services markets to American companies in trade talks next week, adding the U.S. team was heading into them "open-minded."

The discussions between Chinese Vice Premier Liu He, U.S. Trade Representative Robert Lighthizer and Treasury Secretary Steven Mnuchin next Thursday and Friday in Washington will be preceded by deputy-level talks on Monday and Tuesday, Kudlow said on Bloomberg TV.

"Everything's on the table, we'd love to go back to where we were in May when we were a lot closer," Kudlow said.

The Trump trade team hoped to revisit a mostly agreed text from which China had backtracked https://www.reuters.com/article/us-usa-trade-china-backtracking-exclusiv/exclusi v e - c h i n a - b a c k t r a c k e d - o n - n e a r l y - a l l - a s p e c t s - o f - u - s - t r a d e - d e a l - s o u r c e s - i d U S K C N 1 S E 0 W J in May, which led to a breakdown in talks, he said.

The text at that time included an agreement negotiated by Mnuchin that involved the lifting of foreign ownership caps on financial services firms in China.

"I'm not giving you news. I'm just saying we had some pretty good things last spring, like financial services opening - that could be extended," Kudlow said in a subsequent interview on Fox Business Network. "I say 'could' and the president would have to sign off on it, but don't rule out the possibility of good news."

Kudlow declined to make any predictions about the talks but said there had been a "softening of the psychology on both sides" over the past month, with the United States delaying some tariff increases and China making some modest purchases of American farm products.

Kudlow said an impeachment inquiry https://www.reuters.com/article/us-usa-trump-whislteblower/house-begins-trump-im p e a c h m e n t - i n q u i r y - o v e r - c a l l - t o - u k r a i n e - l e a d e r - i d U S K B N 1 W 9 1 O P into Trump's discussions with Ukraine by Democrats in the U.S. House of Representatives was unlikely to affect the trade talks with China.

"I don't think that's an impact right now. I think maybe it has only the tiniest, tiniest effect, maybe occasionally on stock market psychology," Kudlow said.

However, he said the Trump administration continued to monitor freedom and democracy protests https://www.reuters.com/article/us-hongkong-protests/hong-kong-brings-back-colon i a l - e r a - e m e r g e n c y - p o w e r s - t o - q u e l l - p r o t e s t s - i d U S K B N 1 W J 0 5 T , which he said could have an impact on the talks, without specifying how. China-backed Hong Kong authorities have struggled to curb anti-government protests https://www.reuters.com/article/us-hongkong-protests/hong-kong-protesters-go-on- r a m p a g e - t o - d e n o u n c e - p o l i c e - s h o o t i n g - o f - s t u d e n t - i d U S K B N 1 W I 0 2 F that have continued for four months. (Reporting by David Lawder; Editing by Bernadette Baum)