The ‘Gypsy King’ defeated Deontay Wilder in October to retain his WBC title, in what was his first fight in 18 months, but the heavyweight world champion would like a busier schedule next year.
Fury is awaiting the result of an arbitration process that could see the 33-year-old ordered to face mandatory challenger Whyte in the United Kingdom.
A unification bout against Oleksandr Usyk is also on his list of options but the WBA, WBO and IBF champion is set to face Anthony Joshua in a rematch in the spring.
Speaking on talkSPORT, promotor Arum said Fury would prefer to return to the ring in February or March, with a further two bouts scheduled in the rest of the calendar year.
“That is what I would like to see and what he would like to see,” Arum said. “And he wants to do at least three fights in 2022. Hopefully that is how it will roll out and Fury is ready to fight anybody.
“I really believe that Fury is the pre-eminent heavyweight in the world and there is nobody out there that he would be reluctant to fight.
“I think Dillian Whyte should be the next fight for Tyson Fury but there is talk about Usyk who beat Joshua.
“But Joshua is not going to step aside until he is guaranteed the winner of Fury vs Oleksandr Usyk, and how can anybody assure him of that with Whyte in the mandatory position.
“The way I think it will fall out is Fury against Whyte, which I believe Top Rank will co-promote with Frank Warren and can be held in the UK.”