Parker's mother Sala, who helps handle her son's career, said earlier this week she was also still waiting on a verdict.
"I hope they [Higgins and Lonergan] can come up with some kind of solution ... It's entirely up to Dean and David and they will let Joseph know about the outcome," she said.
"The contract is still [for] another year and a half, but if they come up with something different then the contract can terminate on any terms." Parker's trainer, Kevin Barry, refused comment when called in the United States this week.
When approached about progress, Duco Events spokesman Craig Stanaway said the company "hope there is an announcement soon".
"We understand there's a lot of interest. David Higgins and Dean Lonergan are working towards a change in the shareholding in the business," Stanaway said.
"There's still two years to run on Joseph's contract and his view is important in considering the future. Good progress is being made and we hope there is an announcement soon."
In a statement released on behalf of Higgins and Lonergan two weeks ago, Duco confirmed the entrepreneurs were going their separate ways.
The move followed Parker's defence of his WBO world heavyweight boxing title earlier this month - a laboured unanimous points victory over Romanian Razvan Cojanu.
Cojanu was a last-minute replacement for British fighter Hughie Fury, who pulled out less than two weeks before the May 6 bout citing injury.
Englishman Dillian Whyte has emerged as a possible next opponent for Parker as Fury's mandatory challenger position is further undermined by the postponement of his drugs hearing.
It was commonly thought Parker's next opponent would be either Fury or Tony Bellew, but a fight against 29-year-old Jamaican Whyte in September, and probably in London, is looking like a possibility.
Significantly, Whyte's promoter is Eddie Hearn, who also promotes British fighter Anthony Joshua and Bellew, and with whom Higgins gets on well.