At 0721 GMT, commercial banks quoted the shilling at 84.00/20 per dollar, barely changed from Friday's close of 83.95/84.15.
"There is a signature event this week and every eye will be trailed on that," said Raphael Owino, a senior trader at Commercial Bank of Africa.
"Looking at what happened with the inflation there is a possibility of cutting and that could weigh on the shilling."
Kenya's central bank said on its website on Friday it will hold its Monetary Policy Committee earlier than scheduled on July 5 and not July 10.
Inflation, which soared last year to peak at 19.72 percent in November, fell for the seventh straight month to 10.05 percent in June from 12.22 percent in May, and analysts said it pointed to a possible cut in the Central Bank Rate (CBR).
The central bank has maintained a tightening stance since the last quarter of 2011, holding the CBR at an ultra-high 18 percent from December to reign in double-digit inflation and currency volatility.
Traders said they expected the shilling to trade in the 83.60-84.40 range this week, supported by reduced greenback demand in the market.
"With end month out of the way we feel the shilling can now start applying pressure on the dollar in the days to come," said Bank of Africa in a daily report to its clients.