The Vermont senator said he was "very moved" by an invitation to join the April 15 Pontifical Academy of Social Sciences meeting, which will see him take a break from a bruising US presidential campaign.
But while Vatican spokesman Federico Lombardi said Sanders had been invited to the conference, he told AFP that "has nothing to do with the pope" and that no meeting with Francis is planned.
In New York, Sanders told MSNBC that he was "a big, big fan of the pope."
He later told reporters that it was "a possibility" that he would meet Francis, but confirmed that nothing was currently scheduled.
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"It's something that I very much would like to do. The pope's schedule is determined by the Vatican, but I would certainly be enthusiastic about that."
Sanders, who is Jewish but whose wife is Catholic, has frequently expressed respect for Francis, who was treated to a rock-star reception on an inaugural tour of the United States last year.
"We can not, as the pope often tells us, simply be worshippers of greed and money," he told reporters today.
"We've got to create an economy that works for all people and not just the few."
The Pontifical Academy of Social Sciences was established by Pope John Paul II in 1994 to promote the study and progress of economics, sociology, law and political science.
Other conference invited attendees include Ecuador's President Rafael Correa and Bolivian President Evo Morales, the organizers said.
Sanders, who was born and raised in Brooklyn, needs a win in Clinton's adopted home state to help keep alive his dreams of the White House.