The election of the chairman for a two-year term is scheduled for next week.
There are suggestions that Rafsanjani knows he cannot win re-election and is trying to boost an aging clergyman as his successor.
The Mehr news agency reported Monday that Ayatollah Mohammad-Reza Mahdavi-
Kani, who was prime minister almost 30 years ago, has decided to run for the chairmanship.
Mehr quoted Hojatoleslam Mostafa Mirlohi, an aide to Mahdavi-Kani, as saying a majority of the Assembly membership is committed to vote for Mahdavi-Kani and Mahdavi-Kani has decided to run.
But the aide also said Raf-sanjani had contacted Mahdavi-Kani and asked him to run for the chairmanship.
If true, that suggested Ra-fsanjani might try to retain some authority by running for deputy chairman.
Rafsanjani was deputy chairman for decades until the incumbent died and Rafsanjani took over four years ago.
Mahdavi-Kani turns 80 next month. Rafsanjani may be thinking of parking himself behind Mahdavi-Kani until the current political squabbles blow over and he may have a chance to return to the chairmanship.
Mahdavi-Kani succeeded Rafsanjani as minister of the interior in 1980. In 1981, after the bombing assassination of President Mohammad-Ali Rajai and Prime Minister Mohammad-Javad Bahonar, Mahdavi-Kani served as prime minister for two months until Mir-Hossain Musavi took that post.
Mahdavi-Kani has been the head of the Jameh-ye Rohaniyat-e Mobarez, the Combatant Clerics Association, a conservative group, since 1979 when its first chairman, Morteza Motahari, was assassinated.
Mahdavi-Kani is generally viewed as a moderate conservative.
Other possible contenders for the chairmanship who have been mentioned in the media are Ayatollahs Ahmad Jannati and Mohammad-Taqi Mesbah-Yazdi, perhaps the two most hardline figures in the national leadership.
Rafsanjani is believed to have been the key figure in the 1989 election of Ali Khamenehi by the Assembly of Experts to succeed Ayatollah Ruhollah Khomeini. The two men had been friends for decades. The status of their friendship now is an open question.
Many believe they have split as Rafsanjani has clearly not been pleased with the political crackdown since the 2009 presidential election. Others think they remain close friends but that Khamenehi feels a need to keep some political distance since Rafsanjani has become an anathema to regime conservatives. As evidence they site instances where Khamenehi appears to have protected Rafsanjani in the last two years.