MUMBAI, Jan 6 (Reuters) - The Indian rupee is likely to open lower against the dollar on Friday after two reports indicated a robust U.S. labour market, prompting worries over the Federal Reserve rate outlook.

The rupee is expected to open at around 82.64-82.66 to the dollar, down from 82.5550 in the previous session. The local currency had its best session in three weeks on Thursday.

Its unfortunate for the rupee that just when it was building a bit of momentum, the market is back to fretting about the Fed, a trader at a private sector bank said

The 2-year Treasury yield rose to an over one-month high overnight and the dollar index jumped on the back of the U.S. private payrolls and jobless claims numbers. Private payrolls rose more than expected and initial jobless claims declined to a 3-month low.

The upbeat labour reports suggested that U.S. rates were likely to remain high for longer. Further, it increased the probability of a 50 basis points (bps) rate hike by the Fed at this year's first meeting.

The probability of a 50-bps hike has now reached 40%, according to the CME FedWatch Tool. A week ago, futures had assigned a one-in-four chance of the Fed upping rates by that size.

The important U.S. monthly non-farm payroll data is due later in the day. If it also springs a positive surprise, we could see these odds rising more, fuelling a dollar rally, analysts say.

The dollar index can recoup more lost ground if the robust jobs report withdraws bets for a smaller 25-bps hike at the Fed meeting on Feb 1 in favour of a 50-bps hike, DBS Group Research said in a note.

Meanwhile, Kansas City Fed leader Esther George said on Thursday she sees rates holding above 5% into 2024.

KEY INDICATORS: ** One-month non-deliverable rupee forward at 82.74; onshore one-month forward premium at 12.5 paise ** USD/INR NSE January futures closed on Thu at 82.56 ** USD/INR January forward premium at 8.5 paise ** Dollar index at 105.06 ** Brent crude futures up 0.9% at $79.4 per barrel ** Ten-year U.S. note yield at 3.71% ** SGX Nifty nearest-month futures flat at 18,062 ** As per NSDL data, foreign investors sold a net $296.9 mln worth of Indian shares on Jan. 4

** NSDL data shows foreign investors sold a net $52.3 mln worth of Indian bonds on Jan. 4 (Reporting by Nimesh Vora; Editing by Janane Venkatraman)