The Rupert Murdoch-owned paper claims that the store will sell the forthcoming new Google-branded tablets, as well as models from Android partners Samsung and Asus.
Google's Android has built a dominant share in the worldwide smartphone market, but tablets running the operating system lag far behind Apple's iPad.
The new store is being viewed as an attempt by Google to address this shortcoming by creating a sales hub purely for sales and promotion of Android tablet products.
Google declined to comment on the report.
The search giant previously launched an online hardware store for the first Android phone, the Nexus One, in early 2010. But sales were modest as customers preferred to get new handsets direct from mobile operators or other outlets.
However, Google is thought to be more confident with its tablet store because the devices are not so tied to mobile data contracts, as they are often used to access the internet over Wi-Fi networks.
Another key factor is that Google is soon expected to complete its multi-billion dollar takeover of Motorola Mobility, the maker of smartphone and tablet devices.
Google is widely rumoured to be readying its first tablet device for the first half of this year, with reports suggesting that this will be a small screen device to take on Amazon's cheap Kindle Fire.
However, the tablet market is getting hugely competitive as many different firms attempt to catch up with Apple's dominant iPad.
Alongside competing devices running Android, Google will also have to deal with the challenge of Microsoft's Windows 8 operating system, which is optimised for touchscreens and will launch in October.
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