The Times, citing "people with direct knowledge of the matter," said that an agreement could be struck as soon as this week, although it cautioned that the talks could still fall apart.
The Dow Jones-owned blog All Things Digital, citing "sources close to the situation," said Google has offered $5.3 billion for Groupon, in what would be its largest acquisition ever.
Google purchased display advertising company DoubleClick for $3.1 billion in 2007 and mobile advertising network AdMob for $750 million earlier this year.
Google is presently seeking to acquire ITA Software, a flight information software company, for $700 million, but the deal has not yet received the green light from US antitrust authorities.
A Google purchase of Groupon would also likely come in for scrutiny.
European Union competition watchdogs on Tuesday formally opened an antitrust probe into Google after rivals accused the Silicon Valley giant of rigging the online search market.
The Chicago-based Groupon, founded in 2008, offers discounts to its more than 12 million members on retail goods and services, offering one localized deal a day.
All Things Digital said a Google acquisition of Groupon would "move the search giant instantly to the top spot in local commerce online and give it huge troves of data about consumer buying habits and merchant information across the globe."
The Times said Internet portal Yahoo! was also interested in purchasing Groupon but its offer of two billion dollars was rejected as too low.
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