"I aint going to say attack don't let the media make u believe that was terrorist that did it," the 20-year-old Eccleston wrote on Twitter on Sunday, the 10th anniversary of the attacks in the United States.
He also made a reference to O.T.I.S., which can mean "Only the Illuminati Succeed."
The tweet followed another posting in which he called the attack an "accident."
"R.I.P all 9-11 victims my thoughts are with their family's and all those that was affected by this tragic accident!" Eccleston wrote.
The comments were removed from Twitter, and Eccleston then tweeted: "If you don't like what I have to say un follow me !!"
"The club takes this extremely seriously," American-owned Liverpool said Wednesday. "Senior club officials have informed Nathan Eccleston that we are undertaking an investigation into the circumstances surrounding these postings and will decide on an appropriate course of action pending that inquiry."
Eccleston has yet to play for the first team this season. He made his first-team debut in a League Cup match against Arsenal in October 2009.