Kagan, if confirmed, would be the fourth woman on the country's highest court and, at 50, the youngest member who could have a voice on U.S. jurisprudence for decades.
U.S. President Barack Obama was to announce the nomination Monday, several media outlets reported, all citing unnamed sources.
Obama has been seeking a replacement for Justice John Paul Stevens since Stevens, 90, announced in April his intention to resign at the end of the current Supreme Court term. Stevens has been on the court since December 1975.
Kagan's selection isn't expected to alter the philosophical balance of the court if she replaces Stevens, who has led the more liberal side of the court. But she will be the first person in decades nominated to the court who isn't coming from a judgeship, and a lack of published judicial opinions and legal writings leave most of her stances unknown.
She missed out on a chance to join the federal appeals court when the U.S. Senate in 1999 never voted on her nomination by U.S. President Bill Clinton. She served as a clerk for Justice Thurgood Marshall. She graduated from Harvard Law School, where she later served as dean from 2003 until joining the Obama administration as solicitor general.