"We both connected again yesterday and my message was Parker would fight Joshua next and Hearn's message was Anthony Joshua would fight Parker next," he said.
"So it's really down to a question of the deal and money."
Higgins said any agreement had be a fair one and be respectful of Parker having earned a world title.
He said there's no cut-off date for the negotiations.
"It's a moving feast," he said.
"We will do a deal when it's the right deal."
Parker's last fight was in September, when he defended his world title by beating British opponent Hughie Fury by majority decision in Manchester to take his record to 24-0. He won't fight again until the new year.
If the Joshua fight fails to eventuate, unbeaten Australian Lucas Browne looks the likely alternative.
Higgins said talks had been in progress for several weeks with Browne's promoter and terms were largely agreed in principle.
"We could look at pushing the go button on that fight if we decided it was the right option."
Other possible opponents for Parker were American Bryant Jennings in Las Vegas in March and China's Zhang Zhilei in China in the second quarter of the year.
