* Dollar index rises 0.25 percent in European trade

* Optimism about Greece debt proposals starting to wane

* Australian and New Zealand dollars gain after China move (Releads after China reserve cut, fresh quotes)

By Anirban Nag

LONDON, Feb 4 (Reuters) – The Australian and New Zealand dollars rose on Wednesday after China announced a cut in banks’ required cash reserves, adding more liquidity to spur growth in the world’s second-biggest economy.

The 50-basis point reduction in the reserve requirement, which had been expected for some time, was the first industry-wide cut since May 2012, and came after China’s economic growth slowed to 7.4 percent in 2014 – the weakest in 24 years – from 7.7 percent in 2013.

The move lifted currencies linked to China’s growth. The Australian dollar was up 0.3 percent on day at $ 0.7815 by 1145 GMT, strengthening from around $ 0.7785 before China’s announcement. The New Zealand dollar rose to $ 0.7422 from around $ 0.7380, up 0.8 percent on the day.

“Traditionally easing measures from China would have fed through and provided some support for the Australian dollar and New Zealand dollar,” said Ian Stannard, head of European FX strategy at Morgan Stanley (Xetra: 885836 – news) .

“And given that we’re in this bit of corrective phase for the dollar, that may well be the case in the very short term.”

Earlier, the New Zealand dollar bounced from recent four-year lows after central bank Governor Graeme Wheeler said in a speech he expected interest rates would stay on hold given the New Zealand economy remained strong. That disappointed some investors who had expected a more dovish tone as some other central banks including Australia have cut interest rates.

The dollar index rose, recovering some ground after suffering its biggest one-day fall in over a year on Tuesday. It was helped in part by a jump in Treasury yields and by expectations for upbeat U.S. economic data later in the day.

The dollar index was up 0.3 percent at 93.853, having shed 0.9 percent on Tuesday, its biggest one-day fall since October 2013.

Investors trimmed long dollar positions and booked profits but that may be coming to an end given expectations of monetary policy divergence between the United States on one hand and the euro zone and Japan on the other.

The euro’s recovery, driven by expectations that Greece may secure a new debt deal, showed signs of running out of steam. With EU policymakers appearing cool to Greek proposals, optimism regarding a deal could soon fade, traders said.

The euro was down 0.3 percent at $ 1.1440.

“We have seen a shakeout of some stale long dollar positions and lightening of short euro positions on hopes of a new Greek deal,” said Jeremy Stretch, head of currency strategy at CIBC World Markets.

“The dollar bid bias remains in place and if we continue to see good jobs data as well as earnings improve in the United States in the coming days, that could bring the shine back to the dollar.”

Investors were awaiting the monthly ADP private payrolls and ISM non-manufacturing figures due later on Wednesday. On Friday, U.S. non-farm payrolls data will be released. (additional reporting by Jemima Kelly; Editing by Susan Fenton)