Allegations over a purported incident on the plane emerged in the USA media just days after 41-year-old Angelina Jolie filed for divorce from Pitt and sought custody of their six children.
However, on Thursday, the LAPD denied any involvement in the case.
A number of law enforcement sources have told the website it's nearly certain no charges will be brought against Pitt, as there is no way to prove conclusively that he deliberately hurt son Maddox.
"It's unfortunate that people involved are continuing to present him in the worst possible light", the source said.
Sources familiar with the allegations, but not authorized to speak publicly, say the child welfare investigation centers on Pitt's conduct toward his son Maddox, 15, during an argument on the September 14 flight.
After it was revealed that Brad is reportedly being investigated by the Federal Bureau of Investigation for child abuse after a confrontation whilst drunk on a private jet, sources close to the actor have hit out at the "smear campaign" against him.
And the Public Information Officer for the LAPD said: "We don't have anything on Brad Pitt right now".
BRAD Pitt is being investigated by the Federal Bureau of Investigation over claims he flew into a drunken rage on a plane and "got physical" with the eldest son Maddox.
Hedlund said his sheriff's deputies were not called to the airport, and International Falls police were also not called.
A source said: "These claims are exaggerated and fabricated".
Multiple celebrity news outlets including TMZ reported that last Wednesday, one day before Angelina Jolie's divorce filing, the "Ocean's Eleven" star was drunk aboard a private jet and became physically and verbally abusive with their kids and that he was ranting and raving on the tarmac when the plane landed.
"I am very saddened by this, but what matters most now is the wellbeing of our kids", Pitt said. "I kindly ask the press to give them the space they deserve during this challenging time".