NEW YORK, Jan 8 (Reuters) - U.S. Treasury yields were modestly lower on Monday in generally thin trading after gains last Friday amid the stronger-than-expected nonfarm payrolls report, as investors looked to this week's government and corporate debt supply and inflation data.

Volume was lower than usual with Japan closed overnight for another holiday and with a light economic calendar.

In late morning trading, the benchmark 10-year yield was down 4.9 basis points (bps) at 3.992%. It hit a three-week high on Friday following the jobs report which showed that the U.S. economy created 216,000 new jobs in December, higher than forecast.

Stan Shipley, managing director and fixed-income strategist, at Evercore ISI in New York, said there were a couple of conflicting factors that left the bond market with less clear-cut direction.

He cited sharp price cuts by top oil exporter Saudi Arabia and a rise in OPEC output that should lower inflation expectations and push yields lower.

At the same time, Federal Reserve Bank of Dallas President Lorie Logan warned on Saturday that the U.S. central bank may need to resume raising its short-term policy rate to keep a recent decline in long-term bond yields from rekindling inflation.

"Because of the conflicting factors, the 10-year is sitting at around 4% here and has not moved a lot here," Shipley said. "Until we get firm data such as CPI (consumer price index) on Thursday, there is likely not much movement in Treasuries."

Core CPI, or underlying inflation for December is expected to remain unchanged at 0.3%, while the year-on-year number is seen rising at a lower-than-expected pace of 3.8% from a month earlier, according to a Reuters poll.

Investors are also looking to this week's $110 billion auction of U.S. three-year and 10-year notes, as well as 30-year bonds, including heavy corporate debt issuance. According to Action Economics, there is roughly $30 billion on tap from 14 companies, adding to last week's rush to issue.

"We suspect that supply will once again play an outsized role in dictating the price action," wrote BMO Capital Markets in a research note.

"Both from corporates and with $52 billion in 3s and $37 billion in 10s tomorrow and Wednesday, respectively, we remain biased for higher rates as investors are reminded of the weight of supply at a time when it is still too soon for (Federal Reserve Chair Jerome) Powell to begin the process of bringing rates lower."

In other maturities, U.S. 30-year bond yields fell 3.8 bps to 4.161%.

On the shorter end of the curve, U.S. two-year yields slid 5.8 bps to 4.334%.

A closely-watched metric of the U.S. yield curve, showing the gap in yields between two- and 10-year notes US2US10=TWEB narrowed its inversion to minus 34.5 bps.

This part of the curve has been on a steepening trend, typical when investors expect that the Fed is near the end of its tightening cycle.

On Monday, the U.S. rate futures market priced in a 66% chance of a rate cut in March, according to LSEG's rate probability app. For 2024, traders are betting on about five rate cuts of 25 bps each, putting the year-end fed funds rate at 4%. (Reporting by Gertrude Chavez-Dreyfuss; Editing by Sharon Singleton)