Port Adelaide forward Finlayson directed a homophobic slur towards an Essendon player in the third quarter of the Power's 69-point victory over the Bombers at Adelaide Oval on Friday night.
It is understood an umpire's microphone picked up the insult, which was heard by multiple players, and at least one Essendon player also called it out.
The 28-year-old apologised to the target of his slur post-match, and on Sunday made a formal apology, describing his words as "unacceptable".
Alastair Clarkson received a $20,000 fine and a suspended ban in his recent homophobic slur case.
A punishment hasn't been settled, with the AFL still working through options, but chief executive Andrew Dillon confirmed on Monday it would be determined before the next round of games from Thursday.
Last month, North Melbourne coach Clarkson was fined $20,000 and handed a suspended two-match ban for abusing St Kilda defenders Jimmy Webster and Dougal Howard during a pre-season game.
Clarkson was asked to explain his actions to the AFL after allegedly using the homophobic slur "c*******er" during the practice match.
Kane was asked in a segment on the AFL's website if it was reasonable to assume Finlayson wouldn't be suspended, given the precedent that had been set with the Clarkson penalty.
"The really important thing to note here is the consistency with vilification matters is how seriously we take them," she said.
"They're incredibly important integrity investigation processes for us because this is not something we want to hear or see on the field, off the field, or in fact in society, and we take all vilification matters incredibly seriously.
"In terms of comparing and contrasting, we investigate all these matters individually and we make sure that any sanction is connected to the incident that we are investigating and that we are dealing with.
"And that's what we'll be doing here in the Jeremy Finlayson matter."
Andrew Dillon says the AFL takes all vilification cases 'really seriously'.
Earlier on Monday, Dillon was asked how Finlayson's comment measured up to a racial slur.
In 2021, Adelaide forward Taylor Walker received a six-game ban for uttering a racist remark about a rival reserves player.
"We take them all really seriously and I don't think you can compare and contrast," Dillon said.
"But all of them are different, we don't like them and that's why we're looking into it and that's why there'll be an accountability."
Essendon forward Kyle Langford felt the use of a homophobic slur was similar to racist remarks.
"It shouldn't be any different to any kind of racial slur," Langford told 3AW's Wide World of Sports on Monday night.
"It's not acceptable and Jeremy (Finlayson) has owned up to it, so good on him, but the AFL will deal with it."
Kane and Dillon stressed the AFL did not tolerate homophobic vilification.
"I don't think there's any place for that anywhere, let alone the league," Dillon said.
"We take this really seriously and I would prefer to run a proper investigation and a proper process to get to the right outcome."
Asked whether a punishment for Finlayson should be a "captain's call" made by him, Dillon indicated that lay with Kane and general counsel Stephen Meade.
Dillon was speaking at a post-Gather Round press conference, where the AFL and the SA government announced the Barossa Valley would host a game in 2025.
