SINGAPORE, June 26 (Reuters) - The dollar was firm on Wednesday and trading on the precipice of the 160 yen barrier as investors turned cautious and counted down to the release of U.S. price data at the end of the week.

The euro eased marginally overnight and was steady at $1.0708 in Asia trade. At 159.71 per dollar, the yen's level has markets on alert since that is only a whisker shy of where Japanese authorities likely stepped in to buy yen in April.

A surprise jump in Canadian inflation that showed up in data released on Tuesday also injected some nerves into otherwise placid foreign exchange trade, sending the Canadian dollar briefly spiking to a three-week high.

"The May (data shows) that monetary policy’s normalisation is likely to prove protracted and eventually result in a return to near neutral policy, not an expansionary setting," Westpac senior economist Pat Bustamante said in a note to clients.

Markets are banking that Friday's U.S. data shows annual growth in the Federal Reserve's favoured core personal consumption expenditure index slowed to 2.6% in May, the lowest in more than three years and opening the way to rate cuts.

Policymakers, however, continue to signal they are in no rush, with Fed Governors Lisa Cook and particularly Michelle Bowman stressing that decisions will depend on data.

"Inflation in the U.S. remains elevated, and I still see a number of upside inflation risks that affect my outlook," Bowman said.

The Australian dollar dipped 0.1% to $0.6640 and the New Zealand dollar similarly slipped to $0.6115, with small moves reflecting thin trade.

Citi said this week that its etraders found interbank FX volumes some 40% lower than thirty-day averages.

Sterling was steady at $1.268, while bitcoin has recovered somewhat from a dip below $60,000 this week to trade at $61,668.

Along with the yen, China's yuan is also getting squeezed by the dollar's stubborn strength. China has seemed to signal some tolerance for a cheaper currency by gradually weakening the midpoint of the yuan's daily trading range on the dollar.

The yuan has hugged the low side of its band for months and was last at 7.2884 per dollar in offshore trade.

"The yen moves more, and yuan moves are more controlled, but they seldom move in opposite directions," said Societe Generale strategist Kit Juckes.

"If USD/JPY does break through 160 in the coming days, preventing further yuan weakness would be very difficult indeed."

(Reporting by Tom Westbrook; Editing by Stephen Coates)