The World No.1 has been reluctant to state his vaccination status, and now that unvaccinated players have been officially banned from the event, Djokovic will have to make a decision regarding his participation.
"His team have been well aware of this," Todd Woodbridge said on WWOS radio.
"The Australian Open entry list closes six weeks in advance of the tournament, so that's the 6th of December. But the reality is if he wants to play the ATP Cup and have preparations in Australia, he's going to have to have had that jab probably this week."
Australian Open tournament director Craig Tiley said he was under no illusions of Djokovic's desire to compete.
"I know he wants to be here, he'd like nothing more," Tiley said. "He doesn't want to start the year without the opportunity to win all four grand slams - that's enough motivation. So the question is going to be: where is he at with his vaccination status?"
Tiley said he didn't know if the Serbian superstar had a plan to get the jab, and that they hadn't spoken about it.
"At the end of the day, you want to give everyone the best possible chance to get in, and to do it within the parameters which we can," added Tiley. "We've got to still process the visa, and also process the exemption."
Djokovic would have to get on a charter flight between December 27 and January 3, and test negative to the virus upon arrival.
"Time is running out, and obviously you can get one vaccination - the Johnson & Johnson shot - but if you need a double vaccination, that window between the two vaccines is really closing."