Both are due Thursday, and investors have adopted a wait-and-see attitude, leaving major currencies mostly range-bound recently.
With the ECB, investors will be watching for any clues of an imminent slowdown to its bond buying program.
The Bank of Canada on Wednesday left its key interest rate unchanged as expected, and said it would maintain its current policy of quantitative easing. It also reiterated its guidance that rates would remain unchanged until at least the second half of 2022.
The Canadian dollar rose against the greenback, which fell 0.2% to C$1.2087 in the wake of the BoC announcement.
The dollar index fell 0.1% to 90.080, with the euro up 0.18% at $1.2193.
The message that's begun to resonate with investors is that central bank policymakers are going to "brush off high short-term prices," and that's led to a lower U.S. dollar, said Adam Button, chief currency analyst at ForexLive in Toronto.
"The inflation numbers are going to run hotter than what they anticipate in the short term, but there's a rock-solid central bank consensus around transitory inflation," he said.
The dollar rose 0.1% against the yen to 109.61 yen, while sterling fell 0.3% to $1.4122.
The pound slid as Britain and the European Union failed to agree on solutions to post-Brexit trade problems in the British province of Northern Ireland, and exchanged threats in a standoff that could claim the G7 international summit.
Deutsche Bank's Currency Volatility Index hit its lowest level since February 2020 on Tuesday, and sank further on Wednesday. The U.S. dollar index was parked at 90.005.
Graphic: Sleepy FX markets -
While the ECB is expected to keep policy settings steady, the euro could be sensitive to changes in the bank's economic forecasts or any signal that the pace of bond buying could be reduced in months ahead.
Investors are also watching negotiations in Washington over potential infrastructure spending, which could have an effect on the pace of U.S. growth as well. On Tuesday, President Joe Biden broke off talks on an infrastructure bill with a key Republican senator and reached out instead to a bipartisan group.
Bitcoin recovered from a three-week low it hit on Tuesday when signs of institutional investor caution and regulatory attention drove selling. It was last up 4.1% at $34.805.
(Additional reporting by Ritvik Carvalho in London; Editing by Edmund Blair and Jonathan Oatis)
By Caroline Valetkevitch