At 0720 GMT, commercial banks posted the shilling at 87.65/75 per dollar, barely changed from Friday's closing rate of 87.60/70.
A senior trader with a leading commercial bank said the currency would trade in a narrow band of 87.50-88.00 with corporate demand for dollars and inflows from exports like tea determining its likely course.
The shilling has been largely stable this year as risks posed by frequent bomb and grenade attacks, blamed on Islamists, were balanced out by stable economic fundamentals.