At 0948 GMT, commercial banks quoted the shilling at 2,660/2,670 to the dollar, unchanged from Friday's close.
The shilling has gained about 1 percent against the dollar this month, helped by a pause in the central bank's rate-cutting cycle.
However, it is vulnerable to downside pressure due to the suspension of aid by some key donors over corruption allegations and concerns a general election in March in neighbouring Kenya might unleash violence that cuts off vital trade routes to landlocked Uganda.
Analysts said a securities auction on Wednesday could boost dollar inflows and relieve downside pressure on the shilling, at least temporarily.
"If a significant amount of dollar inflows come through from offshore investors in the Treasury bill auction this week, then we might see the shilling remaining at the current levels," said Catherine Jamwa, chief treasury manager at Centenary Bank.
The central bank is scheduled to auction 100 billion shillings ($37.45 million) worth of Treasury bills of all maturities on Wednesday.
"We expect the shilling to trade in a range of 2,670/2,710 in the coming days due to the usual end-month dollar demand from importers, manufacturers and commercial banks," Jamwa said.
Policymakers held the central bank's key lending rate at 12 percent this month, potentially supporting a recovery in yields on government debt and reviving offshore investors' interest in the debt market. The bank had cut interest rates between June and December.
During the last auction on Jan. 9, the weighted average yields on 182-, and 364-day Treasury bills rose although the rate on the benchmark 91-day Treasury bills inched down.