The European Central Bank pumped nearly half a trillion euros into the euro zone financial system last month and is due to make a second offer of three-year loans in February.
Excess liquidity in the system is 415.645 billion euros, according to Reuters calculations.
But concerns over the debt crisis have prompted banks to hoard that cash, depositing 443.701 billion euros at the ECB overnight.
A drop in overnight borrowing to 4.8 billion euros from 15 billion euros provided some relief that year-end funding pressures were easing but analysts warned against reading too much into it.
"It still remains a market that is moribund," Padhraic Garvey, head of investment grade debt strategy at ING, said. "Counterparties don't view each other any differently today than they did a couple of months ago."
The three-month spread between Libor rates and overnight index swap rates , an indicator of financial stress, inched 1 basis point higher to 89 bps. In December the spread reached its widest since March 2009 at 93 basis points.
Markets are pricing in a tightening in the spread between forward rate agreements versus overnight rates, a forward-looking measure of counterparty risk, on the prospect of further monetary easing and more ECB liquidity.
But Simon Peck, rate strategist at RBS, said the ECB move helped short-term liquidity needs but did not address the underlying solvency problems. "We are playing that with a bet against the tighter forward FRA/OIS," Peck added.