Australia captain James Horwill will learn by this evening whether he is available for Saturday's series decider against the British and Irish Lions in Sydney.
Horwill was cleared of any act of foul play by the original hearing eight days ago only for the International Rugby Board to contest the decision.
While Mew has no specific deadline by which to make his decision, the ARU is expecting a verdict this evening with Horwill scheduled to appear at a press conference at the team's Sydney hotel at 11pm (BST).
The appeal took two-and-a-half hours - 90 minutes shorter than the original hearing - and was conducted by video conference call.
Horwill brought his foot down on to Jones' head in the third minute of Australia's 23-21 defeat at Suncorp Stadium, and the Lions second row required stitches in a wound above his eye.
A disciplinary hearing held 24 hours later determined that on the balance of probabilities that there was no act of foul play.
The IRB reacted by announcing on Thursday that following an extensive review of the case it would appeal. Under regulation 17.22.2, the IRB has the right to appeal disciplinary decisions but has never invoked the rule for a not guilty verdict.
"Given its duty to preserve player welfare at all levels of the game, the IRB is compelled to further examine potential acts of foul play which either potentially or in reality impact on the preservation of player welfare," read an IRB statement.
The ARU were disappointed by the IRB's intervention, while the Lions were forced to deny suggestions that they had put pressure on the global game's governing body to act.