The Bronx borough president’s chair is still warm, and the Benjamin Franklin Reform Democratic Club is trying to figure out who’s going to sit in it next.

The Riverdale-Kingsbridge-area political club hosted beep hopefuls Assemblyman Ruben Diaz Jr. and City Council Majority Leader Joel Rivera at a meeting last week. Both men explained their qualifications for current Bronx Borough President Adolfo Carrión Jr.’s job and didn’t debate directly, according to people who attended the meeting.

Ever since Mr. Carrión’s slip of the tongue at a speaking engagement at Yale last year, it’s been widely rumored that he will go to Washington, D.C. to head the Office of Urban Policy under President Barack Obama.

As of press time there was still no official announcement from Mr. Obama’s office about such an appointment.

If Mr. Carrión leaves, Mayor Michael Bloomberg would have to call a special election — but since no announcement has been made, Ben Franklin leaders have postponed any endorsement until their annual meeting at the end of this month.

This state of limbo is touchy for the candidates as well as the club. Mr. Rivera has filed paperwork with the Campaign Finance Board to freeze his campaign committee for Bronx borough president, according to the CFB’s Web site.

He did not return calls requesting comment by press time.

A CFB spokesman said Mr. Rivera’s move would allow him to preserve his over $207,000 war chest for a run at citywide office in 2013, and that contributions in that pile from city residents would remain eligible for matching funds. He’d lose that eligibility if he didn’t freeze the committee.

Since Mr. Rivera has already spent $179,236, according to city filings, and City Council candidates can only spend $161,000 during a campaign, he’d have to start a new committee if he wanted to seek re-election to the City Council.

The board has not yet ruled whether or not Mr. Rivera could un-freeze the finances for his borough presidency campaign in the event Mr. Carrión does leave and Mayor Michael Bloomberg calls a special election to replace him.