Reuters is checking the report.
At 1055 GMT, the rouble was up around 2 percent from Wednesday's close against the dollar to trade at 42.33 after opening the session around 0.7 percent lower.
It gained around 2.2 percent from the previous close to trade at 53.41 versus the euro after also opening sharply lower.
Several traders in Moscow and London cited an article citing the UNIAN agency that President Vladimir Putin and President Petro Poroshenko may have reached an agreement on Crimea as the reason behind the move in the Russian currency.
A forex trader said there could have also been a change in the central bank's interventions policy ahead of its rate meeting on Friday.
Analysts said that positive headlines on Russia-Ukraine gas talks could also be behind the sharp correction in the rouble.