"It is in the nature of a warning," said the director's barrister Elle Nikou Madalin, according to AAP.
"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 wilful blindness."
Nikou Madalin noted that Gibson could start paying the fine by instalments and would then only be open to contempt action is she refused to pay or couldn't afford it.
However, Gibson's lawyer Andrew Tragardh opposed the application, saying only two letters had been sent to his client and there were other avenues to enforce payment.
"This is an unusual, extraordinary and very serious application without proper basis," Mr Tragardh said.
Justice Debra Mortimer is set to deliver her ruling on the application at a later date.
At the time the original fine was served, the judge described Gibson as "cavalier" and having a "relentless obsession with herself".
Gibson had faced a maximum penalty of $1.1 million.