SINGAPORE, May 17 (Reuters) - The dollar headed for its biggest weekly fall versus the euro in two-and-a-half months on Friday as signs of cooling inflation and a softening U.S. economy raised the prospect of rate cuts.

The euro is up 0.8% on the dollar this week, has broken above resistance around $1.0855 and traded as high as $1.0895 in the wake of slowing U.S. inflation.

It was last at $1.0856.

April's annual U.S. inflation numbers met expectations but were lower than the month before, fuelling confidence that the Federal Reserve will cut interest rates in September and again in December - driving rallies in stocks and bonds and pressuring the dollar.

U.S. retail sales were also flat in April and softer-than-expected, and manufacturing output unexpectedly fell.

"(Besides inflation) a lot of activity data has been cooling off," said Westpac strategist Imre Speizer, contributing to selling of the dollar.

At the same time, even though markets price European rate cuts beginning in June, recent data has shown some upside surprises. Germany's economy grew more than expected last quarter and investor morale is at a two-year high.

The Australian and New Zealand dollars are each up sharply on the U.S. dollar this week, with the kiwi up 1.5% and eyeing its best week of the year.

At $0.6663, the Aussie was knocked from a four-month high as a surprise rise in unemployment figures seemed to curtail any risk of another rate hike

Largely disappointing

Chinese data

on Friday was also a drag: factory output topped forecasts but retail sales slowed and home prices fell at their fastest pace in more than nine years.

China announced sweeping steps to rescue the crisis-hit property market at midday on Friday, including cutting mortgage rates, and investors expect

more measures

to be unveiled later in the day.

The New Zealand dollar was down slightly on Friday to $0.6111 with traders looking ahead to next week's central bank meeting, where the official cash rate is expected to stay at 5.5%.

China's yuan was slightly weaker at 7.2246 per dollar on Friday and broadly steady for the week.

Sterling is up 1% this week to $1.2655. The Japanese yen has been broadly steady at 155.78.

In cryptocurrency markets bitcoin is up 7% this week to $65,519.

Later on Friday ,final European CPI numbers will be published and hawkish Bank of England policymaker Catherine Mann is due to make a speech.

(Reporting by Tom Westbrook; Editing by Sonali Paul and Kim Coghill)