According to The Times, the flyer offered "free legal support".
Leigh Day, which was cleared of wrongdoing over claims against British troops in Iraq, said it had "no prior knowledge" of the poster.
At least 80 people died in the blaze on 14 June, leaving hundreds homeless.
According to the newspaper, the poster featured British passports and included two personal email addresses for the members of staff.
It reportedly read: "Our aim is to help you kick-start any potential insurance claims and review any complex documents.
"We do not charge for the assistance we provide. However a third party may charge for their services."
The government recently said it would not conduct immigration checks on foreign nationals who survived the fire, as well as those coming forward with information.
Leigh Day said it does not represent any survivors of the fire and that an internal investigation is under way.
A spokesman for the firm said: "Leigh Day would never have given authority for the posters or their display and we are taking this matter extremely seriously.
"As soon as the posters were brought to our attention, a full internal investigation was commenced under formal protocols," he added.
A law firm has suspended two paralegals over allegations they produced a poster offering to "kick-start" insurance claims for those affected by the Grenfell Tower fire in West London.