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.
The issue is under investigation by US congressional committees and the Department of Justice.
Sources said to be close to the Google investigation said the company was looking into a group of adverts that cost less than $100,000 (£76,000).
Google said in a statement: "We have a set of strict ads policies including limits on political ad targeting and prohibitions on targeting based on race and religion. We are taking a deeper look to investigate attempts to abuse our systems, working with researchers and other companies, and will provide assistance to ongoing inquiries."
Microsoft said on Monday it was also investigating whether any US election adverts had been bought by Russians for its Bing search engine or other products.
A spokesman told Reuters it had no further information at the moment.
Facebook said in September that it had uncovered a Russian-funded campaign to promote divisive social and political messages on its network.
It said that $100,000 was spent on about 3,000 ads over a two-year period, ending in May 2017.
Facebook founder Mark Zuckerberg later said his company would pass the information to US investigators.
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