The two companies have had conversations for several years, but a more serious round of acquisition talks began two months ago, the report noted.
According to the publication, the firms have discussed a price and are negotiating the details, but have not yet signed an agreement.
The report said the size of deal could be more than $500 million. Yelp has raised $31 million in venture capital and is on track to bring in about $30 million in revenue this year.
The company was founded in 2004 by two PayPal veterans, Jeremy Stoppelman and Russel Simmons and dominates the market for reviews of local businesses and ads in big American cities, and has listings in Canada and Britain.
However, the daily said the deal between Google and Yelp could still unravel, particularly if another acquirer comes forward now that details have leaked.
Google has been showing greater interest in the local business market in the United States. It has expanded its profile pages for local businesses, which include location and maps and reviews from other web sites.
In June, Google gave local businesses the ability to manage what people see on their profile pages, similar to what Yelp does.
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