A company spokeswoman confirmed a report in Dutch newspaper NRC Handelsblad that had cited an internal video sent to staff by chief executive Glenn Fogel.
In an e-mail response to questions, Booking said it was trying to save as many jobs as possible.
"Unfortunately, as a result of the crisis, we, like so many other travel companies, need to take the extremely difficult step to reduce our global workforce, with up to 25% of the global employee base intended to be impacted."
The Nasdaq-listed company is based in Norwalk, Connecticut, and has a major office in Amsterdam, Netherlands, where it employs 5,500.
(Reporting by Toby Sterling, editing by Louise Heavens and Jane Merriman)