"We are still pushing for neutral officials ... and I'd say Eddie would be agreeable to that.
"The gloves and ring size are still yet to be agreed on. We are working every day on the deal and I hope to board a flight next week to finalise it."
Higgins said he had enlisted the help of Wladimir Klitschko's lawyer and contract blueprint for his fight against Joshua last April to make sure he got the best deal for 25-year-old Parker, who is set to fight in front of a crowd of 80,000 and television audience of millions in March or April next year.
"Hearn has made a grave mistake in agreeing to this fight," Higgins said, "because Joe is about to slaughter his glass goose.
"It is a very exciting time for Joe's fans, especially his supporters in New Zealand and Samoa."
If Parker is successful in what will be one of the sporting highlights in the world next year, he will be the holder of three of the four recognised world heavyweight titles and will be on the brink of some even bigger paydays.
He told the Herald earlier this month that one of his aims was to set up himself and his family financially for life. "That would be a great achievement I think, he said.