* Euro steadies near 2-month highs before inflation data
* Sterling extends rally as deal likely on Irish border issue
* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh
LONDON, Nov 30 (Reuters) - The U.S. dollar steadied on Thursday but was set for its biggest monthly drop since July as investors grew cautious about the outlook of the world's biggest economy while the euro held near a two-month high before European inflation data.
Though third quarter economic growth in the U.S. was revised up to 3.3 percent on an annualized basis, market participants grew wary about the outlook for U.S. interest rates after next month's much anticipated rate hike.
"The upside for the dollar looks limited for now and euro/dollar is set to rise as the growth story in Europe gathers momentum," said Morten Helt, a senior FX strategist at Danske Bank who expects the euro to strengthen to $1.25 against the dollar over the next 12 months.
The dollar index, which gauges the greenback against a basket of six major rivals, was steady on the day at 93.219 but was down 1.4 percent for November, its biggest drop in four months.
The staggered progress of U.S. tax reform legislation also overshadowed the impact of upbeat economic data on the dollar to some extent.
Congressional Republicans scrambled on Wednesday to reformulate their tax bill to satisfy lawmakers worried about how much it would expand the federal deficit, as the measure moved toward a U.S. Senate floor vote later this week.
"Aside from the good economic data, I think most investors are focused on the tax bill," said Jeff Kravetz, regional investment strategist at U.S. Bank Wealth Management.
"If it does pass, that should give a lift to the dollar, because tax reform is what investors have been focused on for most of the year."
With euro zone business and consumer confidence hitting their highest since the turn of the millennium, traders will turn their attention to the release of European inflation data for November which will provide a glimpse of whether economic growth is feeding into price pressures.
The euro added 0.1 percent to $1.1860, poised to gain 1.9 percent for the month though shy of a two-month peak of $1.1961 scaled on Monday.
Sterling was the star performer in early trading with the Times reporting that Britain is close to a deal over the Northern Ireland border issue.
That puts it on track for posting its best three-day rolling performance in nearly two months.
With the Times citing EU sources preparing to offer a two-year Brexit transition deal as early as January, traders bought the British currency though gains were capped after a 2 percent jump from Tuesday's lows.
Sterling was up 0.4 percent at $1.3455 in early trades and was just below a fresh two-month high of $1.3480 hit in the Asian trading session.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.bi z / c m s / ? p a g e I d = l i v e m a r k e t s (Reporting by Saikat Chatterjee; Additional reporting by Lisa Twaronite in TOKYO, Editing by William Maclean)