Amazon is considering an expansion into this Seattle high-rise, at 8th and Westlake Avenues.

Amazon.com has been growing like crazy — adding 4,200 people worldwide in the first three months of this year alone. And despite a gigantic new headquarters campus, the Seattle company appears to need even more space to accommodate all that growth.

We’re hearing from people in Seattle’s commercial real estate community that Amazon is on the hunt for still more office space in the city. It’s now eying more than 300,000 square feet of additional space in a 28-story tower south of its headquarters.

It would be a logical step for the company: The building, known as West 8th, is at Eighth and Westlake avenues, across the street from the 1918 Eighth Avenue building, where Amazon leased 460,000 square feet of space in March. It’s also on the streetcar line that connects Amazon’s South Lake Union headquarters campus to the city’s downtown retail core.

An Amazon representative declined to comment, and West 8th developer Touchstone declined to address the possibility of an Amazon lease.

By conservative estimates, the more than 300,000 square feet at West 8th could accommodate more than 1,200 people.

Existing major tenants of West 8th are Casey Family Programs and Seattle Children’s Research Institute. Also in the building is Salesforce.com, which leased 11,500 square feet there last year.

Amazon’s headquarters campus, developed by Paul Allen’s Vulcan Real Estate, has been largely completed, with the fifth and final phase scheduled to open in 2013. The main campus will ultimately total about 1.9 million square feet.

Adding in the buildings to the south, the neighborhood is starting to feel almost like a company town. Real estate insiders say Amazon is having an outsized effect on the commercial property market in South Lake Union and the Denny Triangle area to the south, pushing vacancy rates in the neighborhood to less than 13 percent, well below the downtown Seattle average, according to OfficeSpace.com data.

“Aside from Microsoft’s impact in Redmond, I don’t think anything comes close,” said Kip Spencer, OfficeSpace.com co-founder and an adviser to startup tech companies. Spencer said he wouldn’t be surprised to see Amazon expand even further, saying it appears that the company is “just getting warmed up.”

But it may be running out of space in the immediate vicinity of its new headquarters. To find another large block of available space, along the lines of those it has been leasing, Amazon would need to start looking toward the Seattle waterfront, well away from the current South Lake Union streetcar line.

Amazon has been growing beyond its core e-commerce business in recent years through its Amazon Web Services business and Kindle e-reader. The company also is reported to be preparing to launch its own tablet computer.

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