At 0730 GMT, the shilling was at 85.05/15 per dollar, barely changed from Tuesday's close of 85.00/10
"There is good (dollar) selling activity from the NGOs, met by light buys from the petroleum buyers," said Peter Mutuku, a trader at Bank of Africa.
"As we head towards end-month, that's when we could see pressure building on the shilling."
The local currency has largely oscillated around 85 to the dollar, and is up 0.1 percent year-to-date.
Peter Njuguna, head of fixed income at Kenya Commercial Bank, said the central bank's persistent absorption of excess shillings via repurchase agreements (repos) had also helped to stabilise the local currency.
"Overnight rates are catching up with the repo rates. CBK has been aggressively mopping up," he said.
The overnight weighted average rate has steadily risen to 9.4 percent on Tuesday, from 9.2 percent previously, and 6.5 percent on Sept. 17, on the back of the central bank's operations.
On Tuesday, the central bank received bids worth 5.55 billion shillings for the 13 billion shillings it intended to drain out of the market, accepting all bids at a rate of 9.849 percent.