According to TMZ, Kaufman will handle all legal matters during Schwarzenegger's upcoming divorce from estranged wife Maria Shriver.
Kaufman has already entered discussions with Shriver's lawyer Laura Wasser and is "moving forward" with negotiations surrounding the split, the website also reports.
Schwarzenegger and Shriver announced their separation earlier this month after 25 years of marriage following the revelation that the actor and former California governor had fathered a secret love child with a former housekeeper.
It was recently suggested that Shriver could receive a $254 million (£155m) settlement as part of her divorce from Schwarzenegger.
Schwarzenegger may also reportedly be sued by Rogelio Baena, the ex-husband of Mildred Baena, with whom he fathered the love child.