* Euro struggles against dollar after ECB's surprise cut
* U.S. GDP, fewer jobless claims lift expectations of Fed tapering
* Aussie pares gains after rise on upbeat China export data
TOKYO, Nov 8 (Reuters) - The dollar remained buoyant in Asian trade after the European Central Bank's surprise interest rate cut sent the euro to near eight-week lows, but its gains were tempered ahead of the key U.S. payrolls report later on Friday.
A strong jobs report would give the U.S. Federal Reserve a reason to taper its monthly purchases of $85 billion in assets sooner rather than later, particularly after a much better-than-expected U.S. gross domestic product report on Thursday.
"People do not want to get more dollars ahead of today's data, so that's why euro/dollar remains around $1.340," said Masashi Murata, senior currency strategist at Brown Brothers Harriman in Tokyo.
A reduction in U.S. stimulus would contrast sharply with the ECB's accommodative stance. The ECB on Thursday slashed borrowing costs to a record low of 0.25 percent and said it could cut further to prevent the euro zone's recovery from stalling in response to a sharp drop in inflation.
The euro was down about 0.1 percent at $1.3409, after falling as low as $1.3295 on Thursday, according to Reuters data, matching the low set on Sept. 16.
Against the yen, the euro was down slightly from late U.S. levels at 131.60 yen after plumbing a one-month low of 131.18 yen on Thursday.
The dollar gained about 0.1 percent against the yen to 98.15 yen, after a volatile session on Thursday which saw it spike to a near seven-week high of 99.41 yen and drop to a one and a half week low of 97.63 yen.
The dollar index, which tracks the greenback against a basket of currencies, was last up slightly at 80.872, after rising as high as 81.460 on Thursday, its highest since Sept. 13.
Economists polled by Reuters estimated the unemployment rate rose to 7.3 percent in October, while non-farm payrolls likely grew by 125,000 jobs, though the payroll figures would likely show some impact of the 16-day partial government shutdown in the first half of the month.
"The upside risk for the dollar is just as high as the downside risk," said Kathy Lien, managing director of BK Asset Management.
"If payrolls are strong, the string of positive surprises would harden the case for earlier tapering, though we still believe the Fed will move in 2014 and not 2013," she said in a not to clients.
Even if payrolls are weak, she added, investors will expect revisions and a bounce-back in November.
A fall in weekly jobless claims on Thursday likely tipped expectations toward the positive side. Initial claims for state unemployment benefits fell 9,000 to a seasonally adjusted 336,000 last week. Economists polled by Reuters had expected first-time applications to fall to 335,000.
Other data on Thursday showed the U.S. economy expanded at a 2.8 percent annual rate in the third quarter, the quickest pace since the third quarter of 2012, beating economists' expectations of a 2.0 percent growth rate.
But inventory gains accounted for 0.8 percentage point of that growth, which economists say suggests third-quarter growth could evolve to slower growth in the fourth quarter.
The Australian dollar was up about 0.1 percent at $0.9458 , after earlier rising as high as $0.9482 after bullish export data from China, Australia's biggest trading partner.
China's export growth rose 5.6 percent in October from a year earlier, beating market expectations for a 3.2 percent rise and adding to a run of indicators suggesting that the economy is stabilizing.