At the 1300 GMT market close, commercial banks quoted the shilling at 83.90/84.10 per dollar, barely changed from Wednesday's close of 83.95/84.05.
"There seems to be some demand creeping at below 84.00, but with the central bank mopping up liquidity we expect the shilling to be steady at this level," said Duncan Kinuthia, head of trading at Commercial Bank of Africa.
Traders said they also expected debt auctions to help absorb extra shillings from the market, on top of the central bank's frequent use of repurchase agreements (repos) to drain liquidity.
The bank mopped up 2.65 billion shillings ($31.6 million) at a weighted average rate of 9.96 percent in seven-day repos on Thursday, after it received offers of 7.65 billion shillings for the 8 billion shillings it had offered.
At government debt auctions this week, yields on the two-year bond, six-month and three-month paper inched lower after demand hit 45 billion shillings, well above the 18 billion shillings the central bank had offered.
At the Nairobi Securities Exchange, the main NSE-20 share index shed 0.05 percent to 3,817.70 points, dragged down by Kenya Airways, which tumbled 5.6 percent to 12.80 shillings.
"Kenya Airways announced staff cuts but investors feel that's not enough to remedy its high operational cost that is largely fuel expenses," said Rufus Mwanyasia, an analyst at Tsavo Securities.
In the debt market, the yield on the benchmark 91-day Treasury bills on sale on Thursday plunged 168 basis points to 8.583 percent, falling below the repo rate.
Mwanyasia said he expected subscription rates at coming sales to fall as commercial banks sought better returns in the money market.