* Canadian dollar gains 0.1% against the greenback

* Trades in a range of 1.3366 to 1.3395

* Price of U.S. oil settles 1.2% lower

* Canada-U.S. 10-year spread narrows 3.1 basis points

TORONTO, Jan 10 (Reuters) - The Canadian dollar edged higher against its U.S. counterpart on Wednesday but was holding near its weakest level since the middle of December as oil prices fell and investors awaited U.S. inflation data for clues on the Federal Reserve policy outlook.

The loonie was trading 0.1% higher at 1.3375 to the greenback, or 74.77 U.S. cents, after moving in a range of 1.3366 to 1.3395.

On Tuesday, the currency touched its weakest intraday level since Dec. 15 at 1.3414 as investors took stock of recent weakening in the domestic economy.

"USD-CAD has traded in an extremely narrow range today as traders sit on their hands awaiting tomorrow's key U.S. CPI report for December," said Michael Goshko, senior market analyst at Convera Canada ULC.

Federal Reserve Bank of New York President John Williams said that it's still too soon to call for interest rate cuts as the central bank still has some distance to go on getting inflation back to its 2% target.

The price of oil, one of Canada's major exports, settled 1.2% lower at $71.37 a barrel after a surprise jump in U.S. crude stockpiles raised worries about demand in the largest oil market.

Canadian government bond yields were higher across the curve.

The 10-year was up 4.9 basis points at 3.273%, while the gap between it and the U.S. equivalent narrowed by 3.1 basis points to 76.2 basis points in favor of the U.S. note. (Reporting by Fergal Smith; Editing by David Gregorio)