* After selloff, higher yields attract buying * Treasury to auction $32 bln in 3-yr notes * Fed buys $3.71 bln in notes due 2018-2019 By Karen Brettell NEW YORK, Jan 8 (Reuters) - U.S. Treasuries prices gained on Tuesday as higher yields proved attractive and investors prepared for the first sale of coupon-bearing Treasury debt for the year. Treasuries have sold off dramatically over the past week after lawmakers made concessions in order to avoid the "fiscal cliff" of tax hikes and spending cuts, reducing the safety bid for U.S. bonds. Market participants have also been debating whether the Fed is likely to end its bond purchase program before year end, after minutes from the Fed's December policy meeting released last week showed discord among Fed voting members on continuing the buybacks. The higher yields are likely to help demand for $66 billion in new debt sales this week. "The recent back up creates a buying opportunity," said Sean Simko, portfolio manager at SEI Investments in Oaks, Pennsylvania. The Treasury will sell $32 billion in three-year notes on Tuesday, $21 billion in 10-year notes on Wednesday and $13 billion in 30-year bonds on Thursday. Benchmark 10-year Treasures were last up 6/32 in price to yield 1.88 percent, down from 1.90 percent late on Monday, but up from around 1.70 percent at year-end. Thirty-year bonds gained 16/32 in price to yield 3.07 percent, down from 3.10 percent on Monday, and up from 2.87 percent at year-end. Treasuries also earlier got a safety bid on market talk that France's sovereign debt rating was about to be downgraded. A senior French official told Reuters the rumor was "erroneous." "The initial jump was on the rumor of the French downgrade, but now there is decent buying going on," said Charles Comiskey, head of Treasuries trading at Bank of Nova Scotia in New York. "Maybe there are some shorts in the market that will be forced out, I think the three-year sale will go fairly well," he added. In the "when-issued" market, traders expected the upcoming three-year notes to sell at yields of 0.392 percent, only marginally over where the notes were trading in the secondary market at 0.387 percent. With no large economic indicators on the horizon, Treasuries are expected to stay largely rangebound, albeit in a higher yield range after the past week's push upwards. The next focus for the market is likely to be a new round of wrangling in Washington where lawmakers face tough battles on how to cut spending and reduce the deficit, as the country also pushes up against its debt ceiling. "People are focusing back on the bigger picture, we still have the debt ceiling in front of us, we still have growth but albeit at a slower pace than everybody would like," said Simko. The Fed bought $3.71 billion in notes due 2018 and 2019 on Tuesday as part of its latest quantitative easing program, meant to stimulate hiring by reducing long-term borrowing rates.