Police confirmed a 43-year-old had been arrested near the fire on suspicion of “sending malicious communications and obstructing a coroner”.
The body is believed to have been one of the victims of the tower block fire – which killed at least 12 people.
Daily Star Online has tracked down a Facebook page believed to belong to the arrested man.
Fire engulfs Grenfell Tower
“Does any one know this body laying outside my flat for more than two hours”
Several grisly images of what appear to be a dead body feature on the page.
The man’s Facebook post features the caption “does any one know this body laying outside my flat for more than two hours”.
In the comments section, the man claims he unwrapped the plastic sheeting of the “body bag” which had been wrapped around the man.
The caption is followed by a sequence of five images of a dead man’s face covered in soot – followed by a video of the body bag.
Commenters urged him to call the police, but the man responded “no police”.
When someone asked him “is he ****ing dead” the man replied with a crying face emoji.
Firefighters are seen for the first time inside the 27-storey Grenfell Tower in Latimer Road, White City
A Met Police spokesman said: “A 43-year-old man was arrested near to Latimer Road station at around 6pm on Wednesday, June 14, on suspicion of sending malicious communications and obstructing a coroner.”
The arrest relates to the fire at Grenfell Tower.
The man has been taken into custody at a west London police station.
Families are desperately searching for missing loved ones and have taken to social media in a bid to find them.