Both fighters are unbeaten with Fury 20-0 with 10 knockoutsand Parker 22-0 (18 KO), including a win over Andy Ruiz - on a majority decision in October to capture the WBO belt vacated by Tyson Fury.
No details were given about the fight - which could take place in Auckland - although it is understood that a date in April is preferred by Duco Events, which won the purse bid for the fight earlier this month.
Tyson Fury stunned the boxing world by beating Wladimir Klitschko to take the WBA, IBF and WBO belts in November 2015.
He hasn't fought since and is taking time away from the sport to focus on treatment and recovery from drug use and other personal problems that forced him to relinquish his titles. It will be Hughie Fury's first shot at a world title.