Fifa will announce on Wednesday whether Graham Poll's yellow-card error will be enough to put him out of the World Cup.
Poll booked Simunic three times before finally sending him off
The English referee, 42, booked Croatia's Josip Simunic three times before sending him off in the fiery clash with Australia on Thursday.
Poll also sent off Australia's Brett Emerton and Croatia's Dario Simic.
And Fifa communications director Markus Siegler said: "The referees committee will meet on 28 June to decide who is going to stay and who is going."
Before the tournament, Fifa warned referees they face being sent home if they underperform.
Poll will overcome this situation thanks to his strong personality
Fifa referees chief Angel Maria Villar Llona
He awarded the Socceroos a first-half penalty for handball by Stjepan Tomas but failed to spot an even more blatant handball by the same player after the break.
Mark Viduka also seemed to be bundled to the ground in the box during the first half, while it appeared that Harry Kewell was offside when he scored Australia's second equaliser.
A statement from Fifa referees committee president Angel Maria Villar Llona defended Poll but also conceded he had made a mistake.
The statement read: "Graham Poll is an exceptional referee and a great sportsman, who would be able to overcome the situation thanks to his strong personality and love of the game.
"Thursday evening's 2-2 draw between Croatia and Australia in Stuttgart saw referee Graham Poll make an error.
Viduka had strong penalty waved away but does not blame Poll
"The experienced official is disappointed at having committed the error, the first such mistake in his 26-year career.
"The FIFA referees committee also recognised the oversight and the fact that none of the match officials at the stadium picked up on the error.
"In explaining his actions to the committee, Poll said he incorrectly noted down the name of the Australia number three Craig Moore when booking Simunic for the second time and failed to realise his error."
As well as Poll, English assistant referees Philip Sharp and Glenn Turner, as well as USA's fourth official Kevin Stott and fifth official Gregory Barkey can also expect to learn on Wednesday that they are not being kept on for the rest of the World Cup.