Price was tipped to fight Parker on the undercard to IBF champion Anthony Joshua's last fight before the New Zealander's handlers cleverly moved their man down the WBO route where he beat Mexico's Andy Ruiz for the vacant title.
Duco Events are now looking for their best option for Parker's return to action, which is likely to be in April. They would prefer the fight to be in New Zealand or Samoa.
Price's name comes alongside fellow Brit Hughie Fury and American Jarrell Miller as the leading contenders.
