An edited photograph showed the England Under-21 international with a gun pointed at his head and blood across his face and chest.
The picture was also accompanied by some abusive text on the page, which was created on the social networking site earlier this month.
A Scotland Yard spokesman said: "No formal allegations have been made to us but officers have been investigating the claims made through the club media and social media. Investigations still continue."
Sordell claimed on Twitter earlier this month that he and several of his Bolton teammates were subject to racial abuse during their 2-1 defeat to Millwall.
These claims are also under investigation.