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.
However, Joshua triggered a rematch clause with the Ukrainian, leading to Whyte being called as Fury's mandatory challenger.