* Mixed inflation data from German states pushes yields lower
* Borrowing costs fall 2-3 bps across the bloc
* Italy sells 10- and 50-year bonds in auction
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates prices, adds in Italy auction and a quote)
LONDON, Jan 30 (Reuters) - Borrowing costs across the euro zone came off multi-year highs on Tuesday as early indications left investors guessing on key German inflation numbers due out later in the day.
Regional data from the euro zone's largest economy were mixed early and pointed to a possibly disappointing inflation number for Germany, due out at 1300 GMT.
Having hit multi-year highs on Monday on expectations that the European Central Bank will unwind stimulus, euro zone government bond yields were down 2-3 basis points across the board on Tuesday.
German states released a mixed set of inflation data on Tuesday. For example, consumer prices in Saxony rose just 1.4 percent, much slower than the month before, but similar data in Brandenburg proved solid at 1.7 percent.
This gave rise to speculation that German inflation data for January, due out at 1300 GMT, would fall below expectations. As of now, a Reuters poll suggests consumer prices would rise 1.7 percent from the year before in Europe's largest economy.
"Inflation data from Germany could be the game changer today, we already saw the print from Saxony was disappointing," said DZ Bank analyst Sebastian Fellechner.
The ECB's target is for inflation of just below 2 percent in the euro zone.
"If German inflation readings are weaker, we would enter a consolidation mode as questions are raised on the sustained inflation dynamics in the euro zone," said Fellechner.
Yields across the euro zone have risen sharply in recent weeks as a booming European economy has fueled expectations that the ECB will end extraordinary stimulus sooner rather than later, potentially at the end of this year.
The yield on Germany's 10-year government bond, the benchmark for the bloc, rose from 0.306 percent in the first week of December to an over two-year high of 0.707 percent on Monday. But it dropped on Tuesday to 0.68 percent by midday trades.
After going positive for the first time since late 2015, the yield on the five-year Bund dropped back to negative territory.
This fall in yields comes even as Italy auctioned 7 billion euros in medium and longer-term bonds, including a sale of 50-year bonds.
Despite expectations of volatility in the run-up to a March 4 general election, a strengthening euro zone economy has taken the edge off concerns over the popularity of anti-establishment party 5-Star Movement, and the Italy-Germany 10-year government bond yield spread is still close to tight levels at 138 bps. ,
GDP data for the euro zone released by Eurostat on Tuesday showed 0.6 percent rise for 2017's fourth quarter, up 2.7 percent year on year. (Reporting by Fanny Potkin; Editing by Peter Graff/Jeremy Gaunt)