Formula One CEO Chase Carey is still committed to a 25-race calendar in future and has warned events with "unattractive" deals signed under the previous regime that their places on it are at risk.
Liberty took control of F1 at the beginning of 2017 and has sought out new venues to host races in the future.
The idea of 25 races in a season is unpopular with drivers and teams and it would likely be introduced with a significant tweak to the existing weekend format.
So far the only new race added is the 2020 Vietnam Grand Prix, which will take place in the city of Hanoi.
A proposed Miami Grand Prix has been postponed until 2020 at least, while there is speculation of a return to racing at Dutch circuit Zandvoort.
Carey and F1's commercial director Sean Bratches have previously indicated a willingness to keep the championship's traditional races, but many of these are still tied up in deals negotiated by former boss Bernie Ecclestone.
The British Grand Prix at Silverstone is one classic race that remains uncertain beyond its existing deal.
Speaking during a conference call for Liberty shareholders, Carey said: "We believe there is still potential growth, significant growth, in the promotion segment, during the next few years.
"The growth will be driven by three factors. First, we expect to expand our calendar beyond our current 21-race schedule. The expansion will be modest, but we have been excited by the number, quality and diversity of new locations interested in hosting a race. We are on the right side of the quality of races or fees.
"Every race needs to be great for fans, and be an attractive business proposition. The race we announced in Vietnam last week is a prime example of an event that will provide a great track for racing in a location that captures the world's imagination.
"Second, we expect to replace a few existing races where we inherited unattractive agreements with new events or agreements that are better for racing and provide more value. Third, there is significant long-term value in our higher-end hospitality experience.
"Major events today increasingly rely on those customers willing and able to pay for unique and tailored experiences, both in the corporate and retail end."
Carey also criticised the way events had been run during the Ecclestone era.
"The promotion end of our business has been viewed as more mature than other revenue streams in F1. This perception was fuelled by a lack of investment or freshness by the prior regime in our events. Quite simply, our events became stale, which led promoters to focus on costs as opposed to growth.
"Events today are more valuable than ever, and we have a world class premium event. We need to focus on maximising the value of our events, and communicating that to host locations. We're encouraged that the message is getting through to both existing and potential new host cities."