At 0719 GMT, commercial banks quoted the shilling at 84.80/85.00 per dollar, barely changed from Friday's close of 84.80/90.
"Today we may see the shilling strengthening on bond payments. We expect shilling liquidity to be tight," said John Muli, a trader at African Banking Corporation.
"But end-month demand (for dollars), especially from energy guys, may start coming in as the week progresses."
At debt auctions last week the central bank sold a combined 23.2 billion shillings ($273.3 million) worth of a new 15-year Treasury bond, as well as three- and six-month Treasury bills.
Traders said they expected the shilling to trade in the 84.60-85.20 range in coming days, as an uptick in yields at last week's auction makes it attractive for banks to hold on to the local currency.
On the money market, the weighted average interbank rate inched up for the fourth straight session to 7.0 percent on Friday, from 6.8 percent on Thursday.
"People may start reviewing their expectation on interest rates. There is also 19 billion shillings going out in bonds today," said Duncan Kinuthia, head of trading at Commercial Bank of Africa.