The banner, which had the Spanish phrase “Morelos, tu madre es un colchón” - roughly translated as “your mother is a mattress” - was displayed by Aberdeen supporters during their side’s William Hill Scottish Cup tie with the Gers on Sunday.
Club officials are understood to be probing who was responsible for the offensive banner and how it was allowed into the ground.
Aberdeen are believed to be working with Police Scotland to address a series of issues arising from the cup clash, but have begun their own parallel investigation.
The Pittodrie side confirmed earlier this week that more than 80 seats were damaged beyond repair during Sunday’s clash, with Rangers expected to foot the bill to the tune of around £3,000.
The toilets in the away end at the stadium are also thought to have been damaged on Sunday, and Dons chiefs are urgently reviewing their security arrangements after the Morelos banner was allowed in.
All signs, flags and banner have to be green-lit before being allowed into the stadium.
There were six arrests during the game, which finished in a 1-1 draw, for disorder and incidents involving pyrotechnic devices.
Match commander Superintendent Richard Craig said: “I would like to thank the vast majority of supporters from both clubs who heeded our advice and behaved responsibly.
“It is disappointing that a very small minority of fans chose to ignore the warnings and were in involved in disorderly behaviour.
“They have let themselves and their clubs down. Disruptive behaviour in and around football matches in Scotland will not be tolerated and those who choose to conduct themselves in such a way will be firmly dealt with.”
The replay will be held on March 12 at Ibrox. Aberdeen have been allocated just 850 tickets for the tie - competition rules dictate the Dons should be allocated 10,000 briefs for the game.
The Light Blues took around 2,000 fans to Pittodrie, around half the 4,000 they would have been granted under the same rules.