* Euro trades at highest since late 2014
* Dollar index hits 4-month low
* Bitcoin bounces after 11 pct fall (Updates prices and market activity to U.S. market open, changes dateline; previous LONDON)
NEW YORK, Jan 12 (Reuters) - The dollar slumped to a more than three-year low against the euro on Friday, as the common currency extended its gains on hopes that European Central Bank policymakers are preparing to reduce their vast monetary stimulus programme.
The euro was up 0.9 percent to $1.2139, on pace for its biggest single-day percentage gain against the greenback in about two months.
On Thursday, the euro rose 0.72 percent against the dollar after ECB policymakers said in minutes of the bank's December meeting that they could revisit their communication stance in early 2018.
Investors took that as a signal that the ECB will wind down its 2.55 trillion euro ($3.10 trillion) bond purchase scheme this year if Europe's economy continues to hum along.
"The latest ECB comments were a bit on the hawkish side, so that's giving more life to the euro," Minh Trang, senior currency trader at Silicon Valley Bank in Santa Clara, California.
The euro found further support after Chancellor Angela Merkel struck a deal with Social Democrat (SPD) rivals on Friday to open government coalition talks, easing months of uncertainty that has undermined Germany's global role and raised questions about her political future.
The euro's rise weighed on the dollar index, which measures the greenback against six rival currencies. The index was down 0.59 percent at 91.313, after slipping to a four-month low of 91.243.
The index pared losses slightly after data showed underlying U.S. consumer prices recorded their largest increase in 11 months in December amid strong gains in the cost of rental accommodation and healthcare, bolstering expectations that inflation will accelerate this year.
"Everyone is waiting for some type of inflation number to materialise," said Trang.
"But, it may be a bit premature to jump on the inflation bandwagon. I would want to see at least a quarter or two of some solid numbers," he said.
Sterling rocketed to its highest level against the dollar since the vote to leave the European Union in mid-2016, after a report that the Netherlands and Spain were open to a softer Brexit deal for Britain.
Sterling was up 0.98 percent to $1.3668.
Bitcoin was 4.8 percent higher at $13,875 on the Luxembourg-based Bitstamp exchange a day after it skidded over 11 percent after the government of South Korea, a crucial source of global demand for cryptocurrency, said it was considering a plan to ban cryptocurrency trading. ($1 = 0.8237 euros)
(Reporting by Saqib Iqbal Ahmed; Editing by Frances Kerry)