* U.S. private-sector posts strong job growth - report
* Dollar index near 3-month low as U.S. bond yields capped
* Emerging market currencies make big New Year gains
TOKYO, Jan 5 (Reuters) - Asian shares inched closer to their record 2007 peak on Friday as U.S. jobs data pointed to firm economic growth although the greenback was soft as the specter of benign inflation capped domestic bond yields.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.2 percent in early trade, with the benchmark index in Australia and South Korea both up about 0.5 percent.
The MSCI index was about 1 percent off the all-time peak it hit in November 2007 of 591.5.
Japan's Nikkei also gained 0.5 percent to a 26-year high.
MSCI's gauge of stocks across the globe has risen 2.1 percent so far this week, on course to log its best weekly performance since July.
The U.S. ADP National Employment Report on Thursday showed U.S. private employers added 250,000 jobs in December, the biggest monthly increase since March and well above economists' expectations of a rise of 190,000.
That helped the Dow Jones Industrial Average sail past the 25,000-mark for the first time. S&P 500 gained 0.40 percent while the Nasdaq Composite added 0.18 percent, both notching record closing highs.
Despite the strong U.S. jobs report, the dollar was soft, hovering just above its three-month low against a basket of major currencies.
The dollar index stood at 91.860, near Tuesday's three-month low of 91.751.
"The dollar looks very weak at the moment. And I think the reason comes down to the fact that U.S. long-term bond yields are very low despite the Fed's rate hikes," said Masashi Murata, senior currency strategist at Brown Brothers Harriman.
The 10-year U.S. Treasuries yield stood at 2.460 percent , below its seven-month peak of 2.504 percent touched on Dec. 21. Even after the Fed hiked interest rates three times last year, its levels are little different from about a year ago.
U.S. long-term bond yields were capped partly by investors' expectations that inflation will remain tame.
The euro held firm at $1.2075, holding its gains so far this week of 0.6 percent and coming within sight of its 2 1/2-year peak of $1.2092 set in early September.
Many emerging economy currencies have gained sharply against the dollar this week as investors look for higher yields.
Since the start of 2018, the Brazilian real gained 2.4 percent, the Mexican peso 1.8 percent, the Indonesian rupiah 1.1 percent and the Indian rupee 0.7 percent.
In commodities markets, oil prices held near their highest level since May 2015, on concerns about supply risks due to unrest in Iran and another decline in U.S. inventories as refining activity hit a 12-year high.
U.S. crude stood at $61.94 a barrel after having risen to as high as $62.21 the previous session.
(Editing by Sam Holmes)