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.
Troops from Britain, France, Poland and the United States marched alongside 10,000 Russian forces while about two dozen world leaders attended the 65th anniversary, the BBC reported Sunday. The parade also featured tanks, ballistic missiles and a fly-over of 127 aircraft.
Russian President Dmitry Medvedev told spectators lessons from World War II "urge us to show solidarity."
"Peace is still fragile and it is our duty to remember that wars do not start in an instant," Medvedev said. "It is only together that we shall be able to counter modern threats."
Victory Day parades involving more than 102,000 service personnel and more than 200,000 veterans were conducted in 36 Russian cities, Russian news agency RIA Novosti reported.
Medvedev said the march on the Red Square "symbolizes our readiness to defend peace, to prevent the revision of the results of the war, to prevent new tragedies."