"Michael Jackson used to tease me on the phone," thesun.co.uk quoted the Gladiator star as saying.
Jackson would change his voice and call him.
Crowe said: "He'd ring me and in a strong voice say, 'There is an emergency and you need to leave the building'."
He added: "I'd ask, 'Who is this?' And he'd say, 'Do not worry Russell, just kidding, this is Michael'."