Kaufman, whose other famous divorce clients include Reese Witherspoon and Jessica Simpson, has already been in touch with Shriver's attorney, Laura Wasser, to "move forward" with negotiations, according to TMZ sources.
Schwarzenegger, 63, announced his separation from former NBC journalist Shriver after 25 years of marriage on May 10.
A week later, reportedly at Shriver's insistence, he acknowledged that he had fathered a child with a longtime household employee over a decade ago.
The couple is believed to have a prenuptial agreement, but it may not stand in light of their long marriage and Schwarzenegger's infidelity.
Their net worth is estimated to be between $200 million and $400 million, meaning their divorce could be one of the most expensive celebrity splits ever.