The duo appear on the list of nearly 2,000 applications for new top level domain names expected to be released under the auspices of Icann, the Internet Corporation for Assigned Names and Numbers.
In some cases individual names, which will provide an alternative to the familiar ".com", have attracted multiple applicants and may have to be assigned via an auction process.
App has attracted 13 applicants, shop has attracted nine and free has attracted five.
Many companies have applied for their own brand name, including Apple, Nike, Nissan, Dell, the BBC and Cartier.
Among those who have not are Starbucks, Coca-Cola and Kellogg.
Others have been more creative, with L'Oreal going for beauty, in competition with two other applicants.
Some of Google's choices touch on the zany, including boo, lol, soy and wow, while it has also appears to have family on its mind with dad, mom, kid and even dog.
Amazon's choices include a cheeky like (which Facebook has not applied for) and several media-related names such as book, game, mobile, music, movie, song, tunes and video.
|Amazon v Google|
|Amazon applied for...
||Google applied for...