A source in England has suggested that Hughie and his father and trainer Peter, who had to get a special dispensation to enter New Zealand due to his criminal record, will arrive in the country on Wednesday, only 10 days from the May 6 fight at Auckland's Spark Arena.
One of the factors that might be galling to Duco is that they and Parker supported Peter's visa application with New Zealand Immigration.
Previously, Peter has said they would like to spend at least a month in Auckland in order to acclimatise and get over the long-haul travel. That was changed to a suggestion the Furys would arrive 16 days before the fight, and after that there was silence.
The lack of communication could unsettle Duco, who have been forced to search for new ways of funding the fight and have already started selling tickets and corporate tables.
But there is little chance of the Furys not coming - Hughie is guaranteed a payday of $1.7m, a 40 per cent share of the purse, with Parker getting 60 per cent - $2.4m.
Parker and his trainer Kevin Barry arrived from their Las Vegas camp this morning, and expressed surprise at the tactics of the other camp.
Parker said: "He's never [dealt with] jet-lag before, so for someone who hasn't done it before, they should be down here acclimatising to the time and all sorts of stuff like that.
"I've done it before so I know what it takes to get my body used to it and I know I will be ready so I'm not sure how they'll react to it but let's see what happens."
Barry said: "Look, there's still two weeks out to the fight, there's plenty of time for them to arrive. We made an offer to them a while back that they could come out here six weeks before the fight.
"Every international team that we've bought out here in the last four years, we've been very, very accommodating to them, we've put them in the best hotels, we've had drivers with them, we've flown them very well and it surprises me that they are leaving it to this late stage to arrive down."
On the whole Parker's opponents been gracious about the support they have received from Duco while in New Zealand and have behaved accordingly. That may be about to change with the arrival of the Furys.
There is a tentative plan for a press conference to be held on Wednesday, but that, too, could be subject to change.