John Hynes and Boston Global Investors is currently tempting the tech giant to cross the river and settle down into what Boston’s Mayor Thomas Menino has branded the Innovation district.

The push is on, especially now that the City of Cambridge has told Google and landlord Boston

Properties to alter expansion plans for the Internet company at 4 Cambridge Center to preserve existing open space. The plan calls for a 25,000-square-foot glass connector between Google’s existing offices and another building that would cut a rooftop garden in half.

Seaport Square on the South Boston Waterfront will eventually have 1.5 million square feet of office space, as well as 320,000 square feet of retail space.

"Of course, the City of Boston is interested in bringing Google here," said John Guilfoil, the mayor’s deputy press secretary. "The real story would be if we weren’t interested. We have an amazing, burgeoning waterfront Innovation district, and Google would be a perfect fit here."