At 0730 GMT, the rouble was 0.2pc stronger against the dollar at 63.18 and had gained 0.3pc to trade at 70.30 versus the euro.
ING Economics analysts expect the ECB to change the forward guidance and signal upcoming cuts, cementing the markets' dovish expectations.
Investors also closely watch the Turkish central bank, which is expected to cut its key interest rate, currently at 24 percent, on Thursday.
Prices for oil, Russia's main export, edged higher amid Middle East tensions and a big fall in weekly US crude stocks.
Brent crude oil was up 0.55pc at $63.53 a barrel.
The rouble also retains support from month-end tax payments that usually prompt export-focused companies to convert their dollar or euro revenues to meet local liabilities.
By Thursday, companies are due to pay the mineral extraction tax, while the profit tax is due to be paid by July 29.
Russian stock indexes were up. The dollar-denominated RTS index was up 0.3pc to 1,343 points. The rouble-based MOEX Russian index was 0.3pc higher at 2,693 points.
Shares at Gazprom, Russia's top gas producer, were up 2.8pc after the Moscow Exchange said the gas company planned to sell its 3pc stake worth $2.3 billion during the day.