MUMBAI (Reuters) - The Indian rupee is expected to see only marginal relief on Friday after a soft U.S. inflation print made it highly likely that the Federal Reserve will opt for an interest rate cut in September.

Non-deliverable forwards indicate the rupee will open at 83.54-83.55 to the U.S. dollar, slightly higher than 83.56 in the previous session.

It is "hardly surprising" that more "good data" on U.S. inflation is bringing only a bit of relief for the rupee, a currency trader at a bank said.

"That is the nature of things now, in that we have become broadly indifferent to what the dollar does overall. The only time range breakouts happen is when there is a big flow and Reserve Bank of India (RBI) decides to allow it."

The RBI has been holding the rupee in a narrow range via regular interventions, making it among the least volatile emerging market currencies.

FED RATE CUT ODDS CLIMB

Elevated odds of a Fed rate cut in September rose further following an unexpected decline in U.S. inflation. The U.S. consumer price index (CPI) dipped 0.1% last month against expectations that it would rise 0.1%.

In the 12 months through June, the CPI rose 3% compared to 3.3% in May.

U.S. Treasury yields and the dollar index dropped following the report.

The U.S. inflation data has firmed up rate cut expectations, ANZ Bank said in a note.

The odds of a Fed rate cut at the September meeting are now at nearly 90%, per the CME FedWatch Tool.

"The US CPI number for June was better than May's (lower). US CPI has settled down to rate-cut territory," ING Bank said in a note.

KEY INDICATORS:** One-month non-deliverable rupee forward at 83.6; onshore one-month forward premium at 7.25 paise

** Dollar index at 104.5** Brent crude futures up 0.4% at $85.8 per barrel** Ten-year U.S. note yield at 4.23%

** As per NSDL data, foreign investors bought a net $261.6 million worth of Indian shares on July 10

** NSDL data shows foreign investors bought a net $77.7 million worth of Indian bonds on July 10

(Reporting by Nimesh Vora; Editing by Sonia Cheema)

By Nimesh Vora