* Euro trades within sight of its Sept high of $1.2092
* Dollar index languishes near 3-1/2 month lows
* Near-term focus on coming Fed minutes and U.S. data
SINGAPORE, Jan 3 (Reuters) - The euro traded within sight of its highest level in three years on Wednesday, underpinned by optimism about the euro zone's economic outlook.
The euro held steady at $1.2055, after rising as high as $1.2081 on Tuesday. That brought it close to the $1.2092 peak set in September, the euro's highest level since early 2015.
After 2017 proved the euro's best against the dollar in 14 years, the single currency started 2018 on a strong note, as European economies strengthened and expectations grew that the European Central Bank will wind down its monetary stimulus.
Euro zone manufacturers ended 2017 by ramping up activity at the fastest pace in more than two decades, a survey showed on Tuesday, and rising demand suggests they will start the new year on a high.
Also supporting the euro was a comment from an ECB official over the weekend. Benoit Coeure said he saw a "reasonable chance" the bank's bond purchases would not be extended beyond September.
A more synchronised global recovery, with economic growth picking up outside the United States, has prompted other countries' central banks to start moving towards tighter monetary policy in recent months, helping bolster their currencies against the dollar.
Against that backdrop, the dollar has retreated broadly at the start of 2018.
The market's focus is on the global trend towards a more synchronised normalisation of monetary policies, said Heng Koon How, head of market strategy for United Overseas Bank in Singapore.
"It's this monetary policy normalisation everywhere that's playing catch-up to the Fed, and that's why the dollar is weak," Heng said.
Against a basket of six major currencies, the dollar stood at 91.894, having touched a 3-1/2 month low of 91.751 on Tuesday.
The dollar held steady at 112.34 yen.
Later on Wednesday, investors will turn their attention to the minutes of the Federal Reserve's December policy meeting, at which the U.S. central bank raised interest rates for the third time in 2017.
The dollar could also take its cues from U.S. economic data in the next few days, including jobs data on Friday.
Currencies of commodity exporters stood tall after oil prices touched their highest levels since mid-2015 on Tuesday.
The Canadian dollar last stood at C$1.2515 per U.S. dollar. It briefly rose to C$1.2500 early on Wednesday, matching Tuesday's peak, which was the loonie's highest level since Oct. 20. (Reporting by Masayuki Kitano; Editing by Richard Borsuk)