Story highlights Biden and Romney were on opposite sides of the 2012 election

They both considered running for president last year

Park City, Utah (CNN) Former Vice President Joe Biden is encouraging onetime rival Mitt Romney to return to public life and run for Senate.

Biden spoke at Romney's ideas summit, an annual gathering of donors and business leaders in Utah.

During a private event Friday night in Park City, Biden called Romney a man of integrity and said he should mount a challenge next year, according to two people in the room.

"By the way, you should run for Senate," one attendee quoted Biden as saying. The comment was quick and off-hand, but the crowd of Romney loyalists appreciated it and applauded.

The two men were on opposite sides of the 2012 election -- Biden as the running mate of President Barack Obama and Romney as the Republican presidential nominee.

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