In the ride-sharing battle of David vs Goliath, smaller, nimbler David may be gaining ground. Number two U.S. ride-hailing company, Lyft, is growing faster and cutting losses faster than its giant competitor, Uber. And this year, the startup will give details on how it plans to take the battle overseas.

A source with knowledge of the company's plans tells CNBC that Lyft is planning to expand internationally and will reveal more in the year ahead. Lyft declined comment on its international plans.

Currently, Lyft competes with Uber's global ambitions through partnerships with local ride-hailing services in other countries. In December 2015, the American startup joined forces with Didi Chuxing in China, Ola in India and Grab in Southeast Asia. They've since been called the "anti-Uber alliance."

Today, Lyft announced that it is changing the nature of those partnerships.

Currently, Didi users in the United States are able to book a Lyft car directly through their Didi app without having to download the Lyft app.

But Lyft told CNBC, "Along with our international partners, we are updating how we serve our users traveling abroad. We will now direct them to download the partner's app in the country they are visiting."

That means Didi or Grab users who open their apps in the United States will receive a message prompting them to download Lyft, and vice versa for Lyft users that open their apps in China or Southeast Asia. The update will take place next week.

It's unclear how users will respond to the change, which essentially asks them to give up valuable screen real estate and storage on their smartphones. The official line from a Lyft spokesperson is that "this will provide travelers with improved functionality and service in local markets."

But it may also foreshadow Lyft's own global ambitions. After the update, Chinese users who have visited the U.S. may bring a Lyft app back home with them to China. Or India. Or Southeast Asia.

Kind of like a reverse takeover orchestrated by the U.S. leader of the "anti-Uber alliance."