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By Dan Wilchins

NEW YORK, Dec 19 (Reuters) - U.S. private equity firms are looking at starting up reinsurance companies, after an active U.S. hurricane season created demand for coverage and stormy financial markets have weakened many potential competitors.

The conversations are still in early stages, but consultants to the insurance industry say their phones are often ringing.

"Before we used to get calls from hedge funds, but now we're mainly hearing from private equity firms," said Andrew Barile, an insurance consultant in Rancho Santa Fe, California.

Hedge funds including Citadel Investments set up reinsurers in 2005, as newly flush funds looked for investment opportunities and harsh hurricanes like Katrina increased reinsurance demand.

But hedge funds are broadly facing massive investor redemptions, and are hardly in a position to pour hundreds of millions of dollars into new companies. George Soros, one of the world's first hedge fund managers, estimates the industry will shrink by a half to two-thirds.

Even reinsurers with no connection to hedge funds still have problems: they suffered significant losses from hurricanes this year. And with the U.S. stock market down by about 40 percent and the U.S. corporate bond market down more than 7 percent this year, reinsurers' investment portfolios have been hit hard.

Anyone starting a reinsurer from scratch, without payouts to make and investment losses to bear, has a real advantage, Barile said.