The World Boxing Council has named Whyte as Fury's mandatory challenger and the two parties have 30 days to agree a deal.
Fury retained his title with an 11th-round stoppage of Deontay Wilder in their third fight on 9 October.
Fury-Whyte is likely to take place in February or March next year, with Cardiff or Manchester potential venues.
After beating Wilder in Las Vegas, Fury had a 30-day window to set up an clash for the undisputed title with Oleksandr Usyk, who beat Anthony Joshua in September to take the WBA, IBF, WBO and IBO belts.
