Sources quoted by the Washington Post say the adverts aimed to spread disinformation across Google's products including YouTube and Gmail.
They say the adverts do not appear to be from the same Kremlin-linked source that bought ads on Facebook.
Google said it was investigating attempts to "abuse" its systems.
US intelligence agencies concluded earlier this year that Russia had tried to sway the election in favour of Donald Trump.
The Russian government strongly denies the claims and President Trump has denied any collusion with the Kremlin.