TREASURIES-US yields tread water ahead of inflation, trade news

June 10 (Reuters) - U.S. Treasury yields were little changed on Tuesday afternoon as markets awaited news from U.S.-China trade talks in London and inflation data that economists expect to show rising consumer prices.

An auction for three-year Treasury notes also showed somewhat tepid demand though markets will be paying closer attention to sales of 10- and 30-year Treasuries later in the week.

U.S. Commerce Secretary Howard Lutnick told reporters talks were going well but could extend into a third day.

In the auction of three-year Treasuries, the bid-to-cover ratio, a measure of investor demand, fell four basis points from last month's auction to 2.52, a result that Lou Brien of DRW trading said in a client note was "a bit weak, not much, a bit."

This week's Treasury auctions of 10- and 30-year notes and bonds are likely to reveal whether appetite for U.S. sovereign debt is weakening among foreign investors wary of a worsening U.S. deficit, according to Gennadiy Goldberg, head of U.S. rates strategy at TD Securities.

Otherwise, markets are in wait-and-see mode, Goldberg said.

"I think markets are really just grinding sideways here," said Goldberg, noting some signs of general optimism in slightly lower yields.

Economists surveyed by Reuters expect the "core" reading of the Consumer Price Index on Wednesday morning, which excludes volatile food and fuel prices, to show an uptick in May of 0.1 point to 2.9% over the prior 12 months, reversing the cooling trend recorded in recent months and weighing on the odds of a Fed interest rate cut in the near future.

Futures markets are forecasting a rate cut at the Federal Reserve's September policy meeting.

Economists at Goldman Sachs said in an analyst note on Tuesday they expected Trump's import duties to cause "a somewhat larger boost" to monthly inflation numbers in the near future and predicted the year-on-year core consumer price index would move back up to 3.5% by December.

The yield on the benchmark U.S. 10-year Treasury note US10YT=TWEB was last down 1 basis point to 4.474%. The yield on the 30-year bond US30YT=TWEB fell 1.5 basis points to 4.939%.

A closely watched part of the U.S. Treasury yield curve measuring the gap between yields on two- and 10-year Treasury notes US2US10=TWEB, seen as an indicator of economic expectations, was at a positive 46.0 basis points.

The two-year US2YT=TWEB U.S. Treasury yield, which typically moves in step with interest rate expectations, rose 0.9 basis points to 4.012%.

The breakeven rate on five-year U.S. Treasury Inflation-Protected Securities (TIPS) US5YTIP=TWEB was last at 2.336% after closing at 2.35% on June 9.

The 10-year TIPS breakeven rate US10YTIP=TWEB was last at 2.303%, indicating the market sees inflation averaging about 2.3% a year for the next decade.