* FTSEurofirst 300 down 0.03 pct, Euro STOXX 50 flat
* Investors eyeing Draghi's press conference on Thurs
* Stock picking to thrive in the next months -Thebault
By Blaise Robinson
PARIS, Oct 2 (Reuters) - European stocks pared early losses and steadied on Tuesday, with investors looking for clues on whether Spain will soon request a bailout that would ease fears of contagion from the euro zone debt crisis.
Alstom tumbled 5.8 percent, the biggest loser among European blue chips, after the French transport and power engineering company launched a capital hike of 350 million euros ($451.68 million) to finance an investment in a Russian rail equipment firm.
At 0821 GMT, the FTSEurofirst 300 index of top European shares was down 0.03 percent at 1,104.54 points after surging 1.4 percent on Monday.
According to senior euro zone sources, Spain is ready to request a bailout as early as next weekend but German officials said Madrid should hold off, creating confusion among investors.
"There are worries over whether or not it will be a bailout and whether such a bailout would trigger credit downgrades," said David Thebault, head of quantitative sales trading at Global Equities.
"But beyond that, markets have not completely realised how powerful the new ECB policy is and how it will reshape things, so there's still upside."
At this week's policy meeting, the European Central Bank is seen leaving interest rates on hold, but investors' focus will be on the tone of ECB head Mario Draghi's press conference.
Draghi's comments in late July - when he said the central bank was ready to do whatever it takes to save the euro - sparked a rally in shares, with the Euro STOXX 50 up 15 percent since then and the euro zone bank index up 42 percent.
"It's time to go back to stock picking, to look for the companies full of cash, the market leaders, and the ones exposed to the zones where economic growth is, such as emerging markets," Thebault said.
Energy stocks were among the main losers on Tuesday, with Repsol down 1.5 percent and Total down 0.9 percent, as crude oil prices remained under pressure due to worries over the demand outlook.
Banking shares were volatile, with Societe Generale down 1.1 percent while Deutsche Bank was up 0.3 percent.
Around Europe, UK's FTSE 100 index was down 0.1 percent, Germany's DAX index was flat and France's CAC 40 was off 0.2 percent.
The euro zone's blue chip Euro STOXX 50 index was flat at 2,499 points, after losing ground in early trade but managing to stay above a key support level, its 50-day moving average, tested on Monday.
For Petra von Kerssenbrock, technical analyst at Commerzbank, the blue chip index remains in a consolidation mode although the medium-term upside trend is still intact.
"The Euro STOXX 50 is in a bottom pattern below the resistance at 2,600-2,611 (a peak hit in March). Short term, the index should see a trading market between 2,330 and 2,600," she said.