"So we wonder whether Joshua at unification level will be found out?"
Higgins said he and Joshua's promoter Eddie Hearn have a few more details to iron out before an official deal is made.
"I'm here to hopefully negotiable and close a deal with Eddie Hearn for the first unification bout in 10 years for Joseph Parker to fight Anthony Joshua for four heavyweight belts.
"Hearn and Joshua want the deal and so do we. We are just working through minor details and we are getting closer every day.
"Will it be announced soon? Maybe, could be announced early next week but we are still going over and back on a few contractual points.
"I am reasonably confident we can make a deal within a week."
Hearn echoed Higgins' thoughts, saying he's hopeful an announcement can be made next week.
"My man David Higgins - he's a bit nuts, David Higgins, but he's a good guy," Hearn told IFL.TV. "He knows what he wants and we're moving at speed.
"We had about four hours yesterday, we're drafting, we've overcome most of the points in the agreement.
"Hopefully, Parker will come in the weekend... hopefully, you'll get an announcement next week."
Meanwhile, both Joshua and Parker have also shared hints of the imminent fight announcement on social media.