As per the reports, WhatsApp is likely to launch the desktop version of its popular messaging clients. However there is no official announcement from the facebook owned company.
On phones, Whatsapp uses your phone number to authenticate you when you set it up for the first time. On the Web, it's likely that it will sign you in the same way. Presuming there's a Whatsapp desktop app or a Web app that you could sign in to in your browser, Whatsapp could send a code to your phone to verify your identity and seamlessly sync your conversations between your phone and your computer. Apple's iMessage service, for instance, works in a similar fashion.