By Ilaina Jonas

NEW YORK (Reuters) - Google Inc, which spent nearly $2 billion for one of Manhattan's largest office buildings, is in the market to rent a bit more space as the company grows and is unable to get some of its tenants out, according to three sources familiar with the matter.

Google is looking to lease between 60,000 square feet to 100,000 square feet of office space, which depending upon the building, could be a floor or two, one source said on Tuesday.

Google paid about $1.8 billion for the 17-story, 2.9 million square-foot building that occupies an entire city block in 2010. The art deco building was constructed in 1932 for what was then called the Port of New York Authority.

The December 2010 sale put the Midtown South office market on the road to becoming New York's technology center.

The company has been a magnet for other technology companies, especially small start-ups, who have clamored to be there and made Midtown South one of the tightest U.S. office markets.

But the building also came with tenants with leases, including Nike Inc, Sloan-Kettering Memorial Cancer Center and Barnes & Noble Inc.

One of the buildings it has looked at is 770 Broadway, the source said.

A representatives from Vornado Realty Trust, which owns 770 Broadway did not return a caller seeking comment. Jordan Newman, a Google spokesman in New York, declined comment.

Other technology and media companies such as Facebook Inc and Microsoft Corp are also in the market for longer-term space in New York City.

(Reporting By Ilaina Jonas; Editing by Leslie Gevirtz)