Mitt Romney's campaign says the two men participated in their first mock debate session last week.
Olson served as solicitor general under President George W. Bush and has argued 58 cases before the Supreme Court, winning three-quarters of those cases.
He has become a staunch advocate for same-sex marriage in recent years and has argued in federal court against California's Prop. 8, which banned gay marriage.
Ryan and Biden will square off in the vice presidential debate on October 11th in Kentucky.