Eager to snap up a company that makes some much-used travel-search technology—and keep it out of Google Inc.'s hands—several potential buyers are circling ITA Software Inc., according to people familiar with the matter.

ITA, whose technology powers a huge chunk of all online travel queries in the U.S., has been negotiating exclusively on a potential deal with Google, which doesn't have its own standalone travel search engine, these people said.

But...