BENGALURU, Dec 27 (Reuters) - Indian shares advanced on Wednesday, tracking gains in Asia and an overnight rally in U.S. stocks, over optimism the Federal Reserve could begin cutting interest rates early next year.

The blue-chip NSE Nifty 50 rose 0.57% to 21,562.85 points, while the S&P BSE Sensex was 0.54% higher at 71,724.64 as of 10:23 a.m. IST. The Nifty 50 is about 30 points shy of its record high hit last week.

The more domestically-focussed mid-caps rose 0.83%, while small-caps gained 0.74%.

"The sentiment is positive and could continue for the remaining few days of the week as generally December is a strong month for the markets," Apurva Sheth, head of market perspective and research at Samco Securities, said.

Sheth pegs the support for Nifty 50 at around 21,000 and resistance at around 21,500.

India's benchmark indexes have gained 6.5% so far this month, helped by strong domestic macroeconomic data, a return of foreign inflows, and a moderation in oil prices.

Indian equities are mirroring gains in Asia and an overnight rally in U.S. stocks amid expectation the Federal Reserve could begin cutting interest rates as soon as March.

Markets are pricing in a more than 80% chance the Fed is likely to begin cutting rates next March, according to the CME FedWatch tool.

Among individual stock moves, Larsen & Toubro hit an all-time high after getting an order to establish renewable generation, power utilities and water systems for a luxury tourism destination in Saudi Arabia.

Power generator SJVN climbed 3.3% after the company won a 100-megawatt solar power project at tentative cost of 5.5 billion rupees. ($1 = 83.2350 Indian rupees) (Reporting by Rama Venkat in Bengaluru; Editing by Varun H K and Mrigank Dhaniwala)