* U.S. sells $35 billion in two-year notes * U.S. home price data improve, consumers turn gloomy * ECB chief Draghi not attending Jackson Hole event * Fed's Fisher says QE3 not "predestined" By Chris Reese NEW YORK, Aug 28 (Reuters) - U.S. Treasuries prices rose on Tuesday as traders anticipated hints from Federal Reserve Chairman Ben Bernanke later this week of possible further monetary stimulus to help the economy. Bets on a third round of "quantitative easing" through large-scale bond purchases, nicknamed QE3, pushed benchmark yields to three-week lows earlier on Tuesday after they touched a three-month high last week. "It appears likely that the market will be spending the fall with a significant probability of QE3 priced in," said Hans Mikkelsen, credit strategist at Bank of America Merrill Lynch in New York. News that Spain's most economically vital region Catalonia was requesting aid and fears the euro zone's fourth-biggest economy might soon need a full-blown bailout also fed safe-haven bids for U.S. government debt, traders and analysts said. Benchmark 10-year notes traded 5/32 higher in price to yield 1.64 percent, down from 1.65 percent late Monday, while 30-year bonds were 9/32 higher to yield 2.75 percent from 2.76 percent. The Treasury sold $35 billion of two-year notes on Tuesday afternoon, with little market impact. "Post-auction the market continues to be extremely quiet with benchmarks little changed from their pre-auction levels," said Justin Lederer, interest rate strategist at Cantor Fitzgerald in New York. The Treasury will sell $35 billion of five-year notes on Wednesday and $29 billion of seven-year notes on Thursday. Bernanke is scheduled to deliver a speech on Friday at a meeting of global central bankers in Jackson Hole, Wyoming. In 2010, he hinted at QE2 at this event. That second round of quantitative easing involved a combined $600 billion purchase of long-dated Treasuries from November 2010 through June 2011. Bernanke's counterpart at the European Central Bank, Mario Draghi, will not attend the annual gathering, citing a heavy workload. Traders had looked forward to a speech from Draghi on clues to how European policy-makers are tackling the region's festering debt crisis. There have been reports in recent days that the ECB is considering a bond purchase program aimed at containing the borrowing costs of Spain, Italy and other debt-laden euro zone members. Doubts have emerged on whether the Fed will embark on another large stimulus program at its Sept. 12-13 policy meeting. Dallas Fed President Richard Fisher told Reuters on Tuesday Fed policy-makers have not decided on QE3. "Nothing is predestined," he said. U.S. economic data on balance since the July 31-Aug. 1 Fed policy meeting suggested some improvement after weakening in late spring and early summer. A modest uptick in jobs and housing reduced expectations for more stimulus. "Bernanke might disappoint this Friday," said Anthony Valeri, fixed income strategist at LPL Financial in San Diego. Tuesday's economic reports reinforced the view of a slowly growing U.S. economy. Homes prices rose for a fifth month in a row in June, according to Standard & Poor's/Case-Shiller, but shopper confidence fell to its lowest in nine months in August. Separately, the Fed on Tuesday bought $4.646 billion in government debt that matures between November 2020 and August 2022. This is the latest part of its "Operation Twist" worth $667 billion aimed at holding down long-term borrowing costs.