* U.S. three-year note auction shows solid results

* Coming up: 10-year and 30-year auctions

NEW YORK, Jan 9 (Reuters) - U.S. Treasury yields were marginally higher on Tuesday, with prices weighed down by upcoming government and corporate bond issuance, and investors anxiously awaiting key inflation reports this week.

The U.S. Treasury sold $52 billion in three-year notes on Tuesday, picking up a high yield of 4.105%, lower than what the market expected at the bid deadline, suggesting investors absorbed the note without a premium.

There was $139 billion in bids for a 2.67 bid-to-cover ratio, a demand gauge, better than the 2.42 last month but fractionally below the 2.69 average.

U.S. 10-year notes and 30-year bonds are on tap for sale on Wednesday and Thursday.

Treasury yields briefly pared gains after the auction, but came back higher again.

"It's pretty choppy right now and we're in this price discovery phase," said Angelo Manolatos, macro strategist at Wells Fargo in New York. "But the main thing that is true right now is that we are at a policy rate peak. The Fed is moving closer to an easing mode."

Thursday's U.S. consumer price index (CPI) for December due out on Thursday will shed further light on when the Federal Reserve could start cutting rates. U.S. producer prices will also be released on Friday.

U.S. core CPI is forecast to remain flat at 0.3% from the month before, while the year-on-year number is seen rising at a lower-than-expected pace of 3.8% from November, according to a Reuters poll.

With inflation seen on a downward trend, U.S. rate futures have priced in a more than 65% chance of a rate cut in March and about five rate decreases of 25 bps each for 2024, according TO LSEG's rate probability app IRPR.

"It (rate cut bet) may be a little aggressive, but I think it's going to happen. Fed cuts are on the table," said Tom di Galoma, managing director & co-head of global rates trading, at BTIG in New York.

"I don't see the Fed waiting and dragging their feet. The Fed is closer to easing than tightening, closer to easing than holding pat."

Federal Reserve Governor Michelle Bowman late on Monday gave a nod to rate cuts. Bowman pulled back from her persistently hawkish view, saying she now sees U.S. monetary policy as "sufficiently restrictive," and signaled her willingness to support eventual interest-rate cuts as inflation eases.

Also weighing on Treasury debt prices and lifting yields a little higher, there is a bunch of investment grade issuance from 10 additional firms, on top of the 50 companies that have priced since 2024 began, according to Action Economics on Tuesday. That was also pressuring Treasury prices, which move inversely to yields.

Wall Street dealers typically look to lock in borrowing costs for corporate bonds they are underwriting. As part of that process, a dealer sells Treasuries as a hedge to lock in the borrowing cost on the bond issue before the deal is completed. Once the bond is sold, the dealer buys Treasuries to exit the "rate lock."

Analysts said there has been a lot of corporate supply in Europe, as well such as Spain, Italy and Belgium and that has also spilled over to the U.S. Treasury market.

In afternoon trading, the benchmark 10-year yield was slightly up at 4.017%. Since hitting a five-month low of 3.783% on Dec. 27, the 10-year yield has gained about 12.5 basis points (bps).

On the shorter-end of the curve, the two-year yield climbed 2.3 bps to 4.368%.

Post the three-year note auction, U.S. three-year yields were up 2 bps at 4.139%. (Reporting by Gertrude Chavez-Dreyfuss; Editing by Marguerita Choy and Will Dunham)