Pitt's partner Angelina Jolie is a well-known supporters of the Reds, as his the couple's son Maddox.
In comments reported on Liverpool's official website, Pitt remarked: "I have some friends who are very close to Liverpool, so if I went another way I might be disowned."
NBA star LeBron James is another high-profile supporter of the club and is actually a minority shareholder.
He recently attended Liverpool's entertaining 1-1 draw with Manchester United - after he described the day as 'one of the single best experiences of my life' on his Twitter page.
"That came from the simple fact of how passionate and loyal those fans are," he continued.
"But to walk through the facility the day before - to see all the history and achievements was very powerful.
"Liverpool have won 18 league championships and it meant a lot to read about King Kenny and Steven Gerrard - a hometown kid who now captains the team.
"And then to be at Anfield and see 40,000 fans screaming at the top of their lungs, the whole game was an unbelievable experience for me.