* ANZ Group slumps on regulatory investigation

* U.S. inflation data due for Wednesday

* Energy stocks lose most in about 2 weeks

May 13 (Reuters) - Australian shares closed flat on Monday, as miners offset losses in banks and energy stocks, while traders exercised caution ahead of the U.S. inflation reading due later this week in their wait for cues on the Federal Reserve's rate-cut policy.

The S&P/ASX 200 index closed 0.01% higher at 7750.000 points. The benchmark closed 0.4% higher on Friday.

The crucial U.S. core consumer price index is due on Wednesday, with hotter-than-expected data ruling out any rate-cut hopes from the Fed.

The bellwether miners ended marginally 0.03% higher in the resource-heavy bourse, as iron ore prices consolidated after hitting a more-than-two-week low on Friday. BHP Group rose 0.8%, while ironore miner Rio Tinto lost 0.8%.

Financials also pared back some of their early losses to close 0.03% lower, with the U.S. inflation reading looming over the rate-sensitive sub-index.

"Banks are one of the most sensitive sectors impacted by the US inflation data this week. Investors are nervous," said Brad Smoling, managing director at Smoling Stockbroking.

Three of the "Big Four" banks ended up in the positive territory. ANZ Group lost 3.2% after reports of the country's corporate regulator investigating the lender emerged.

Energy stocks fell 0.7% as they tracked global oil prices, which fell on signs of weak oil demand, while U.S. rate-cut hopes remained subdued.

Sub-index major Woodside Energy dropped 1.1% and smaller peer Santos lost 0.9%.

Real estate stocks dropped 0.1%, information technology stocks lost 0.6%.

Health stocks, however, gained 0.4% with Australia's priciest stock CSL rising 0.3%.

New Zealand's benchmark S&P/NZX 50 index lost 0.9% to finish the session at 11,652.1600. (Reporting by Rajasik Mukherjee in Bengaluru; Editing by Janane Venkatraman )