* Three-month Euribor rate rises for first time in 3 months
* Money markets give up on the idea of a deposit rate cut
* Eonia, Euribor rates may have bottomed out
By Marius Zaharia
LONDON, Oct 1 (Reuters) - Key Euribor interbank lending rates rose on Monday for the first time in three months as expectations that the European Central Bank could cut interest rates this week are fading.
Money markets are also in the process of pricing out the possibility that the deposit facility rate will ever be cut into negative territory from the current zero percent.
Only a minor chance of such a move is factored in for the start of next year, but some banks are recommending clients to exit such bets or position for a rise in January-dated rates.
Economists polled by Reuters expect the ECB to leave its main refinancing rate flat at 0.75 percent at its meeting on Thursday.
The three-month Euribor rate , traditionally the main gauge of unsecured bank-to-bank lending, rose to 0.223 percent from 0.220 percent.
"This points to more uncertainty creeping into the market with regards to any future rate cuts," said Elwin de Groot, senior market economist at Rabobank.
"Rates are very low already and there's basically only one thing that could push down money market rates even further, and that would be a cut in the deposit rate. But that seems not to be a subject of discussion within the ECB."
ECB Executive Board Member Benoit Coeure said last week that a cut in the deposit rate, a move that would effectively charge banks to hold money with the ECB overnight, may not be beneficial for all segments of the market.
Imposing a penalty for parking cash at the central bank could shake things up in the dormant euro zone money markets and sway banks to take the risk of lending to each other more to get a return on their cash.
Healing money market segments that have been frozen by the euro zone debt crisis is seen as an important step towards restoring sustainable economic growth in the region.
However, the low level of short-term rates is already making some asset managers take cash out of money markets and put it in other assets such as bonds.
The forward Eonia market, showing where investors expect the overnight Eonia rate to be at certain points in the future, is completely dismissing the probability of a deposit rate cut in October.
The Eonia rate dated for the October meeting last traded at 0.09 percent. Eonia has fixed at an average of around 8 basis points over the deposit rate in the past few months.
The lowest points on a forward Eonia curve that covers the ECB's next 12 meetings are January and February at just above 0.05 percent. That compares with lows of about 0.03 percent hit last month.
The 0.5 percent level prices in approximately a 10 percent probability of a deposit rate cut of 25 basis points, according to Commerzbank rate strategist Benjamin Schroeder.
But ECB-dated Eonia rates may have already reached their bottom, analysts say. Societe Generale strategists recommend bets that the January Eonia will rise to 0.07 percent on the view that the ECB will leave the deposit facility rate unchanged.
Rates beyond January may rise because the excess liquidity in the euro zone system, currently at 734.5 billion euros
based on Reuters calculations, may start to shrink next year.
Banks have the option to pay back the cheap three-year loans taken from the ECB in December starting with the end of January.
"Those rates need to price in some sort of premia for the uncertainty ... regarding liquidity conditions," Commerzbank's Schroeder said.
(Editing by Hugh Lawson)
Keywords: MARKETS MONEY/