* German April inflation weaker than expected
* Euro zone private lending slows, money supply weakens
* ECB fails to fully sterilise past bond purchases
* Banks take biggest sum of weekly ECB loans since June 2012
* Cocktail of data compounds ECB headache before May meeting
FRANKFURT, April 29 (Reuters) - A fall in euro zone lending, weaker-than-expected German inflation and signs of tightening in money markets compounded the European Central Bank's policy conundrum on Tuesday as it weighs up whether to act next week.
ECB President Mario Draghi last week identified a weakening of the euro zone inflation outlook and tensions in short-term money markets as potential triggers for fresh policy action.
Official data on Tuesday showed soft inflation in the euro zone's core economy, Germany, while the key overnight money market rate hit a level seen only rarely since 2011 on Monday.
Tightening conditions prompted banks to load up on ECB weekly loans on Tuesday, while the central bank failed to draw sufficient funds to offset its past bond purchases.
"Taken together - the German inflation data, the money market tensions, and the euro, which is still strong - that makes a good case for doing something," Nordea economist Holger Sandte said.
German inflation hit 1.1 percent in April, up from 0.9 percent in March but below a consensus forecast of 1.3 percent.
A preliminary reading on Wednesday is expected to show euro zone inflation at 0.8 percent in April, up from March's 0.5 percent but still well below the ECB's medium-term target of just below 2 percent. Anything less would pile pressure on the ECB to act when it meet in Brussels on May 8.
"More than usual, it depends on the inflation number tomorrow," said Sandte.
Draghi said last week that if the inflation outlook were to deteriorate, the ECB could respond with a "broad-based asset purchase programme", probably quantitative easing, or QE - effectively, printing money to buy assets.
On Monday, however, he told lawmakers from Germany's ruling coalition that while low inflation would persist in the euro zone, he did not expect deflation, according to a source who attended the meeting.
The ECB chief did see "a problem of ongoing low inflation rates, which could lead to measures", the source said, adding: "He mentioned quantitative easing in this context but made clear that we're still some way off QE."
Nordea's Sandte said that, given the ECB's reluctance to go ahead quickly with QE, "to me, it would make sense to cut the main interest rate to 0.125 percent and also cut the deposit rate to send a signal".
The euro zone central bank's main refinancing rate currently stands at a record low 0.25 percent, with the deposit rate it pays banks for holding their money overnight at zero.
The ECB may be closer to making targeted moves to encourage lending to small and medium-size businesses, although that would lack the scale and impact of a broad asset-buying plan.
Previous measures, including cutting interest rates to near zero, pumping liquidity into the banking system and widening the pool of assets it accepts from banks in return for funding, have so far failed to unclog the flow of cash to the real economy.
Lending to euro zone households and companies declined further in March and money supply growth slowed, ECB figures showed on Tuesday.
The central bank is putting the bloc's top banks through a thorough review of their balance sheets, to weed out soured loans, update collateral valuations and adjust capital so that they can lend more freely in future.
Many banks are repaying early loans they took from the ECB at the height of the euro zone crisis, and have set aside tens of billions of euros for the ECB's health check of the sector, leaving them less cash to deposit at the central bank.
That has caused spare cash in the financial system to fall and pushed up money market rates.
Excess liquidity - cash beyond what banks need for their daily operations - fell to around 86 billion euros on Tuesday, according to Reuters calculations, the lowest since before the ECB offered three-year crisis loans to banks in December 2011.
The EONIA overnight money market rate meanwhile hit 0.398 percent on Monday - its highest since 2011 with the exception of two liquidity-tight days late last year and at the end of March.
Highlighting the squeeze, the ECB failed for the third week running to fully offset its past purchases of government bonds, while the 172.621 billion euros of weekly loans banks took from the ECB on Tuesday was the most in a week since late June 2012.
In a Reuters poll, 16 of 19 traders said pressure on money market rates would eventually ease as banks take more money in the weekly ECB operations. The other three said falling excess liquidity would push the EONIA rates higher. ($1 = 0.7223 Euros)
(Editing by Catherine Evans)