Consumer Affairs Victoria said it has filed court documents compelling Ms Gibson to pay her fine or risk prosecution for contempt of court if she doesn't pay the fine.
Ms Gibson was ordered to pay a $410,000 fine last year in October, after the Federal Court found her guilty of misleading and deceptive conduct for falsely claiming she had brain cancer which was cured by alternative therapies and nutrition.
She told the Australian Women's Weekly in April 2015 that she never had terminal brain cancer.
"I don't want forgiveness. I just think [speaking out] was the responsible thing.
"Above anything, I would like people to say 'OK, she's human'."
Ms Gibson has made money off falsely claiming she healed her terminal brain cancer by eating wholefoods, accumulating more than $440,000 from app and book sales.
She claims she donated most of it to charity, but the court found she only gave away $10,000.
Ms Gibson urged to pay in instalments
Consumer Affairs Victoria said Ms Gibson has yet to pay any of the amount owing on the fine, months after it was issued.
Two letters requesting payment went unanswered, according to barrister Elle Nikou Madalin, for Consumer Affairs Victoria.
Consumer Affairs Victoria has applied to amend the court's penalty orders to allow Ms Gibson to be prosecuted for contempt of court, if it is found she has the money to pay the fine, but refuses to do so.
If the application for a Federal Court "endorsement" is granted, it could expose Gibson to a prosecution for contempt of court, if she doesn't pay the fine.
"It is in the nature of a warning," the director's barrister Elle Nikou Madalin said of the application on Tuesday.
"We are now concerned that there may be contempt down the track.
"We don't want to create a situation where down the track Ms Gibson might try to claim willful blindness."
Ms Nikou Madalin said Gibson could start paying the fine in instalments and would only be open to contempt action if she refused to pay when she could afford it.
Ms Gibson's barrister says application is 'without proper basis'
But Gibson's barrister Andrew Tragardh opposed the application, saying only two letters had been received about the fine and there were other avenues to enforce payment.
"This is an unusual, extraordinary and very serious application without proper basis," he said.
Gibson is currently protected from contempt action by a legal clause that could be overruled with an endorsement order, the court was told.
Justice Debra Mortimer will deliver her ruling on the application at a later date.
When the original fine was handed down, the judge described Gibson as "cavalier" and having a "relentless obsession with herself".
Gibson had faced a maximum penalty of $1.1 million, but had the sum reduced to $420,000 after the court determined Ms Gibson had no ability to pay the initial sum.
