* No immediate bank sanctions planned

* G7 summit to focus on China-Russia trade impact on Ukraine conflict

* Russia trade business has moved to small Chinese banks

WASHINGTON, June 9 (Reuters) - U.S. officials expect the Group of Seven (G7) wealthy democracies to send a tough new warning next week to smaller Chinese banks to stop assisting Russia in evading Western sanctions, according to two people familiar with the matter.

Leaders gathering at the June 13-15 summit in Italy hosted by Prime Minister Giorgia Meloni are expected to focus heavily during their private meetings on the threat posed by burgeoning Chinese-Russian trade to the fight in Ukraine, and what to do about it.

Those conversations are likely to result in public statements on the issue involving Chinese banks, according to a U.S. official involved in planning the event and another person briefed on the issue.

The United States and its G7 partners - Britain, Canada France, Germany, Italy and Japan - are not expected to take any immediate punitive action against any banks during the summit, such as restricting their access to the SWIFT messaging system or cutting off access to the dollar. Their focus is said to be on smaller institutions, not the largest Chinese banks, one of the people said.

Negotiations were still ongoing about the exact format and content of the warning, according to the people, who declined to be named discussing ongoing diplomatic engagements. The plans to address the topic at the G7 were not previously reported.

The White House did not respond to a request for comment. The U.S. Treasury Department had no immediate comment, but Treasury officials have repeatedly warned financial institutions in Europe and China and elsewhere that they face sanctions for helping Russia skirt Western sanctions.

Daleep Singh, deputy national security adviser for international economics, told the Center for a New American Security this week that he expected G7 leaders to target China's support for a Russian economy now reoriented around the war.

"Our concern is that China is increasingly the factory of the Russian war machine. You can call it the arsenal of autocracy when you consider Russia's military ambitions threaten obviously the existence of Ukraine, but increasingly European security, NATO and transatlantic security," he said.

Singh and other top Biden administration officials say Washington and its partners are prepared to use sanctions and tighter export controls to reduce Russia's ability to circumvent Western sanctions, including with secondary sanctions that could be used against banks and other financial institutions.

Washington is poised to announce significant new sanctions next week on financial and nonfinancial targets, a source familiar with the plans said.

This year's G7 summit is also expected to focus on leveraging profits generated by Russian assets frozen in the West for Ukraine's benefit.

RUSSIA BUSINESS MOVES TO CHINA'S SMALL BANKS

Washington has so far been reluctant to implement sanctions on major Chinese banks – long deemed by analysts a "nuclear" option – because of the huge ripple effects it could inflict on the global economy and U.S.-China relations.

Concern over the possibility of sanctions has already caused China's big banks to throttle payments for cross-border transactions involving Russians, or pull back from any involvement altogether, Reuters has reported.

That has pushed Chinese companies to small banks on the border and stoked the use of underground financing channels or banned cryptocurrency. Western officials are concerned that some Chinese financial institutions are still facilitating trade in goods with dual civilian and military applications.

Beijing has accused Washington of making baseless claims about what it says are normal trade exchanges with Moscow.

The Biden administration this year began probing which sanctions tools might be available to it to thwart Chinese banks, a U.S. official previously told Reuters, but had no imminent plans to take such steps. In December, President Joe Biden signed an executive order threatening sanctions on financial institutions that help Moscow skirt Western sanctions.

The U.S. has sanctioned smaller Chinese banks in the past, such as the Bank of Kunlun, over various issues, including working with Iranian institutions.

China and Russia have fostered more trade in yuan instead of the dollar in the wake of the Ukraine war, potentially shielding their economies from possible U.S. sanctions.

(Reporting by Trevor Hunnicutt in Washington and Lananh Nguyen in New York Additional reporting by Andrea Shalal and Nupur Anand Editing by Heather Timmons and Matthew Lewis)