The market is divided on whether the central bank might increase interest rates. Fifteen analysts and economists polled by Reuters expect the central bank to keep the key rate at 7.50 percent, while twelve said an increase to 7.75 percent looked possible.
At 0713 GMT, the rouble was 0.3 percent weaker against the dollar at 66.42 and was down 0.2 percent at 75.37 versus the euro.
"In our baseline scenario, we expect the rouble to show limited reaction to the event (the central bank meeting)," analysts at VTB Capital said in a note.
The central bank's rate decision is due at 1030 GMT and will be followed by a press briefing by Governor Elvira Nabiullina who is expected to shed more light on monetary policy.
The central bank is also set to release details of a possible decision to resume foreign exchange purchases for state reserves, which were suspended earlier this year amid increased market volatility.
Nabiullina said last month the central bank could resume foreign exchange buying on the open market on behalf of the finance ministry in mid-January.
Oil prices had a negative impact on Russian assets as Brent crude oil, a global benchmark for Russia's main export, declined 0.6 percent to $61.06 a barrel.
The dollar-denominated RTS index slid 0.5 percent to 1,123.39 points. The rouble-based MOEX Russian index was 0.4 percent lower at 2,368.86 points.