Rangers believe Alfredo Morelos was "racially abused" during Sunday's match against Celtic.
The striker, 23, was sent off near the end of Rangers' 2-1 win at Celtic Park.
"We would expect now that all measures will be taken to identify and deal with those responsible," said a Rangers spokesperson.
Celtic say they have "received no reports of any racial abuse but would fully investigate any should these be brought to our attention".
And Police Scotland say they have received no complaints.
The Ibrox side's victory moved them to within two points of Premiership leaders Celtic, with a game in hand to play in the new year.
Colombia international Morelos was pictured drawing a hand across his neck in an apparent throat-cutting gesture as he left the field following his dismissal.
Celtic said they were "aware of the gestures made by the player towards Celtic supporters".
But Rangers had said in an earlier statement on their website it was "a gesture used commonly throughout South America to indicate quite simply that something - in this case, the match - is finished".