* Lipper data shows funds ditching European equities
* Weak payrolls number would offer some relief
By Toni Vorobyova
LONDON, June 7 (Reuters) - European shares steadied just above six-week lows on Friday, with investors looking to a jobs report later in the session for clues on whether the U.S. economy is strong enough to warrant an easing of equity-friendly stimulus.
After a year-long rally fuelled by global central bank support, equity markets are getting increasingly concerned that the policy cycle could be turning, with the European Central Bank this week saying it is in no rush to launch fresh measures, while U.S. Federal Reserve officials openly discuss when would be the right time to start scaling back quantitative easing.
As such, any signs of strength in the U.S. economy - which is expected to have added 170,000 new non-farm jobs in May - could provide the catalyst for stock market declines, while a very weak number may be a positive.
With so much riding on the data, investors were expected to wait for the release before moving the market significantly in either direction. The FTSEurofirst 300 was flat at 1,178.33 points at 0722 GMT.
“Over the very short run there might be some relief (from payrolls) but the general theme is that ... we seem to be losing our mantra that central banks will help us all the way,” said Gerhard Schwarz, head of equity strategy at Baader Bank.
“We are heading for increased volatility and some kind of topping-out process over the next couple of weeks. But at some point probably there will a 10 percent correction coming into the equity market, and possibly deeper into the third quarter.”
Battered by concerns about the longevity of central bank stimulus, the FTSEurofirst 300 has shed 3.1 percent since the start of the week - on track for its worst week in over a year.
Reflecting the more cautious mood, Thomson Reuters Lipper data showed U.S.-based funds pulling money out of European equities for a second week in a row, with an outflow of some $1.8 billion - the biggest weekly drain since late 2011.
The more narrow EuroSTOXX 50 gauge edged 0.1 percent higher to 2,678.17 points, staying below key technical support around 2,684 points that gave way the previous session.
However, technical charts still showed scope for the market to turn around back towards the recent multi-year highs.