The city manager has been asked to submit Cambridge as a test site for Google’s ultrafast Internet program, in which the company will stretch fiber-optic cable that moves data at one gigabit per second —100 times faster than what most people have, even in Cambridge — to between 50,000 to 500,000 people.

The Mountainview, Calif.-based company, which has offices in Cambridge, has not described its criteria for choosing what communities will get the fiber-optic cable.

Leland Cheung, a city councillor who said Monday he has asked City Manager Robert W. Healy to put forward Cambridge as a possibility, said he’s “cautiously optimistic” but sees good reasons why Google would not choose Cambridge: Mainly that, if you’re going to put a lot of cable some place, you would probably want to avoid the hassles that come with digging up an old, urban and densely populated city. Councillor Tim Toomey also made a request of the city manager.

There’s a buzz around Cambridge about the network, Cheung said, but he’s not sure people should get too excited.

On the other hand, he couldn’t pass up the chance to submit a bid. He was sure others were pushing for a nomination as well within Cambridge, as other communities nationwide — including Rochester, N.Y., and Greensboro, N.C. — are already trying to create a surge of requests, on the possibility a groundswell of requests could sway Google engineers.

Google is taking submissions and nominations from communities through March 26.

This report was updated to include Toomey’s actions.