A Twitter spokesman declined to comment.
With its rooftop garden, gourmet café and airy art deco offices, Twitter has made its mark in the blighted Central Market neighborhood of San Francisco since moving there in June 2012. Other companies soon followed, including One Kings Lane and Yammer.
Bloomberg reports that no lease has been signed for the 1970s building, but Twitter is the only party interested in the property.
Jack Dorsey, co-founder of Twitter and of Square, was a driving force behind both companies locating in the Central Market neighborhood. He said he was drawn to the "variety and vibrancy" of city life. The city has also lent a hand to make it a destination for tech companies, offering tax breaks to those that put down roots in the troubled Central Market and Tenderloin areas.
The high-tech industry is bringing a dramatic surge in economic activity not seen in San Francisco since the height of the dot-com boom more than a decade ago. Not everyone is thrilled about that.