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.

Ma, 27, becomes only the fifth man to have won singles titles at the World Championships, World Cup and Olympics.
With defending champion Zhang taking silver, China have claimed nine of the last 12 Olympic men's singles medals.
Japan's world number six Jun Mizutani beat Belarusian Vladimir Samsonov 4-1 in the bronze medal match.
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Bill Palmer, from Southampton, called the Alex Dyke show on BBC Radio Solent about his life after his wife went into a nursing home.
Dyke immediately ordered a taxi to bring Mr Palmer to the studio to allow phone-in listeners to chat to him.
A recording of the call has been viewed tens of thousands of times on Facebook.
The 95-year-old, from Sholing, married his wife Sheila, 85, on 2 June 2014 after they had been friends for 30 years.
Shortly afterwards Sheila - who has dementia and colitis - fell and was taken into hospital. She was then moved into a nursing home, where she now lives.
Mr Palmer phoned the BBC Radio Solent programme on Wednesday during a phone-in on "Love - later in life".
Although he visits his wife every day, he said: "Every day is hell. I feel so alone".
The production team immediately arranged to take Mr Palmer to the studio in Southampton, where he sat in on the rest of the show.
Mr Palmer said: "I just sit with my wife and we tell each other we love each other, and that's it.
"She knows who I am and she often says 'we did get married on the second of June didn't we?' - and that's when it hurts.
"I listen to the radio and watch TV and have lots of friends, but unfortunately when you get old people don't visit - that's life."
Listeners phoned in to offer support and advice to Mr Palmer.
He was offered Sunday lunch, afternoon trips out and a ukulele orchestra to play for him, but he kindly turned them all down.
"I didn't know such kindness existed," he told one caller.
Dyke said Mr Palmer had "touched the hearts of thousands of listeners" and it was his "nicest moment in 30 years of broadcasting".
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.
[NEXT_CONCEPT]
China's world number one Ma Long beat countryman Zhang Jike 4-0 to win the men's singles and claim a table tennis Grand Slam.
[NEXT_CONCEPT]
A 95-year-old invited into a BBC radio programme after calling in about being lonely has become a hit on social media.