At 0630 GMT, the shilling was posted at 85.25/45 per dollar, barely changed from Thursday's close of 85.30/50.
"We are seeing a bit of demand from energy guys, but that is well matched from flows from non-governmental organisations (NGO's) and exporters," said Dickson Magecha, a trader at Standard Chartered.
Magecha added that rising yields were also offering support for the local currency.
Yields on government debt have been inching up, drawing in local investors who had previously shunned the debt market due to the low returns, instead preferring the returns on central bank liquidity mop-ups or the equity market.
Magecha said rising yields had made it expensive to fund long dollar positions or buy forward contracts.
In last week's auction, the benchmark 91-day Treasury bills rose to 10.346 percent at a heavily oversubscribed auction from 10.237 percent the previous week.
Raphael Owino, a senior trader at Commercial Bank of Africa, said he expected the shilling to stay steady in the coming days despite the central bank slashing official rates by 200 basis points to 11 percent on Wednesday.