MUMBAI, Jan 11 (Reuters) - The Indian rupee held a narrow range around a key psychological level on Thursday, as traders gauge whether the currency has room to strengthen further following the U.S. inflation data.

The rupee was at 83.0150 to the U.S. dollar at 10:50 a.m. IST, compared with 83.0250 in the previous session. Its intraday range has been between 82.9850 and 83.0525.

The rupee has had a good beginning to the New Year, reaching a near one-month-high of 82.97 on Wednesday.

"While USD/INR is looking to break 83, the possibility of durable INR strength will be more estimable post today's (US inflation) data," said Srinivas Puni, managing director at QuantArt Market Solutions.

"The Federal Reserve could find it difficult to aggressively cut rates if inflation refuses to taper off towards the 2% objective."

Investors have priced in a total of 140 basis points of Fed rate cuts in 2024, nearly double what the U.S. central bank indicated in its dot plot. A few economists reckon investors' expectations may be a tad optimistic.

"We think that future inflation reduction will be slower to achieve and that some central banks, particularly the Fed ..., will need to proceed cautiously with regards to setting policy direction," ANZ said in a note.

The U.S. inflation update is expected to show headline consumer prices rose 0.2% month-on-month in December, while the core measure increased 0.3%. On a year-on-year basis, core prices are estimated to have increased by 3.8%, compared to a 4% rise in November, providing more evidence of easing inflation.

The data will give cues on not just how many rate cuts the Fed will opt for this year but also on when it could deliver the first of those. (Reporting by Nimesh Vora; Editing by Savio D'Souza)