The boxers' respective management teams were scheduled to meet today and finalise an agreement involving the financing of the fight and pay packets.
But this has now been extended, although there has not been any indication as to why.
Speaking to ESPN, WBC president Mauricio Sulaiman said: "We have extended for one week the free negotiations, per their request."
If a deal can't be agreed in this time, the rematch, which was the WBC's unanimous choice, will go out to the highest bidder.
This means there is a big chance rival promoter Eddie Hearn could sensationally win the purse bid and broadcast the show on his DAZN franchise in the US.
But that seems unlikely at this stage, with Wilder and Fury, as well as their respective promoters Shelly Finkel and Frankm Warren, all keen to agree a deal for Part II.
The two warriors fought out a thrilling draw, with many believing Fury had been cheated out of completing one of the greatest boxing comebacks.
Fury, 30, challenged for the WBC strap in LA and he outboxed Wilder, 33, for much of the fight.
Despite having to rise from the canvas twice, Fury bemused the champion with a stinging jab and well executed right hand.
As the Brit looked to have ripped the belt away from Wilder, the fight was declared a split decision draw, much to the disapproval of Fury and Warren.
The judges ruled the contest a draw, after harsh scores of 115-111, 112-114 and 113-113.
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