The store will sell Google-branded tablets as well as models made by Samsung and Asus, claims the Wall Street Journal.
It is being widely seen as an attempt to win back market share from Apple, which dominates the tablet sector.
Google declined to make any comment on the report.
Google had mixed success with its first online hardware store. That sold the first Android phone, the Nexus One, to consumers in early 2010.
Sales of the phone via the web store were sluggish and were quickly outstripped by the numbers of handsets sold through mobile operators and other stores. Online sales were ended in mid-2010.
This time, Google is said to be hoping to fare better because of the way tablets tend to be used – ie in the home and on domestic wi-fi rather than on the street and depending on a mobile network.
This may also have made operators reluctant to push tablets because customers are not using them on mobile networks.
Fierce competition
Another influence on the decision could be the fact that Google is poised to take control of Motorola’s mobile division, which will give it the ability to manufacture its own handsets and tablets.
Google will have to sell a lot of tablets to catch up with market leader Apple. Figures compiled by analysts Gartner suggest 70% of all tablets sold are iPads.
No date has been set for when the online store might open, said the WSJ, quoting people familiar with the project.
Google has a diminishing opportunity to launch the store because competition for tablet customers is getting fiercer all the time.
Amazon launched a touch screen Kindle e-reader in the US in late 2011 and the gadget will come to Europe in late April.
In addition, Microsoft’s Windows 8, which is optimised for touch screens, is expected to be launched in October 2012.