Rankine, if found guilty, could be suspended for ladder-leader Adelaide's looming finals campaign.
The AFL has previously handed down suspensions ranging from three to five games to players guilty of homophobic slurs.
The top-placed Crows have one home-and-away game remaining and can't finish lower than second entering the finals.
Adelaide officials have refused to name Rankine as the player under investigation.
But it's known the brilliant forward/midfielder is at the centre of the probe.Â
"We are aware of an alleged matter involving one of our players in Saturday night's game and we are in discussions with the AFL," a Crows spokesman said on Monday.
The AFL confirmed an investigation but also didn't name Rankine.
"The AFL is aware of an alleged matter, with the AFL integrity unit making enquiries," the league said in a statement.
Rankine allegedly directed a slur at a Collingwood opponent in Saturday night's clash at Adelaide Oval, which the Crows won by three points.
The AFL this year banned West Coast's Jack Graham for four games after he admitted a homophobic slur against a GWS opponent in round 17.
Last year, Gold Coast's Wil Powell was suspended for five matches and Port Adelaide's Jeremy Finlayson was banned three games, both for making homophobic comments to opponents.
Any ban for Rankine, renowned as among the league's most talented players, would be a hammer blow to Adelaide's finals campaign.
The Crows will enter the finals in top spot if they defeat lowly North Melbourne on Saturday.
Adelaide will then host two finals as club returns to the playoffs for the first time since losing the 2017 grand final.
Rankine, 25, is yet to play a final. He spent three seasons with Gold Coast before the Adelaide-born playmaker joined the Crows at the end of the 2022 season.
Last Monday, Rankine spoke of his excitement at Adelaide's finals campaign.
"I have never been this high on the ladder before so it's quite nice," he told reporters.
"We'll appreciate it ... it's nice to think about, but we know we have some more steps to take throughout the year."
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