The news was first reported by The Washington Post.
Kerrey has not officially made an announcement or filed paperwork to run. Paul Johnson, a former campaign manager of Kerrey's, denied the reports to the AP but said that he's reconsidering his decision.
Kerrey faces a difficult battle for election in one of the most Republican states in the country. He also faces challenges having lived in New York City since 2001 and having not been on the state ballot since 1994. However, his stature gives Democrats some hope for retaining the seat.
The seat first opened up in late December when Kerrey's successor, Sen. Ben Nelson (D-Neb.), announced he would not run for reelection. That decision precipitated speculation that Kerrey would run.
Just weeks ago, Kerrey said he would not run for the seat for family reasons. "I have given the decision of becoming a candidate for the U.S. Senate very serious thought and prayer," he said in an email to supporters on Feb. 7. "To those who urged me to do so, I am sorry, very sorry to have disappointed you. I hope you understand that I have chosen what I believe is best for my family and me."
Kerrey served in the U.S. Senate from 1989 to 2001. Upon leaving the Senate, Kerrey served as the president of The New School, a university located in Greenwich Village in New York City, leaving in 2010. Kerrey ran for the Democratic nomination for president in 1992.
University of Nebraska Regent Chuck Hassebrook and attorney Steven Lustgarten have announced they are running on the Democratic side. State Attorney General Jon Bruning, state Treasurer Don Stenberg, state Sen. Deb Fischer, investment adviser Pat Flynn and Air Force Veteran Spencer Zimmerman are running on the Republican side.
In an interview with the AP in January, Kerrey admitted the odds are not in his favor. "I would say if you bet ... you'd have to bet against me," he said. "I've been away 11 years. I'm a Democrat. Obama's going to top the ticket, and he's probably going to be unpopular. So I'd say the odds are probably not good."
HuffPost Politics brings you the top political stories three days a week. Learn more