Claims that Mojtaba Khamenei leads Iran and is being sought by the CIA and Mossad remain unverified.
The assertions link his reported rise to an alleged US-Israeli attack that supposedly killed his father, Ayatollah Ali Khamenei.
One account places his purported assumption of the supreme leadership on 8 March.
The reported date of the alleged attack is not consistent across the accounts, with another account placing it on 28 February.
The accounts say he has not appeared publicly for months and that no authenticated audio or video statement from him has been presented.
They allege that he has avoided phones, computers and other electronic communications, using written messages delivered by trusted intermediaries instead.
Former Mossad official Rami Igra said that, if such communications exist, identifying a close intermediary could be key to locating him.
Suggested locations include underground facilities in Tehran and a possible military site near Qom, but neither location has been established.
Former Mossad official Avner Abraham alleged that Iran may be using lookalikes as part of his security arrangements.
His reported health and status are disputed: one assertion says US intelligence assesses that he is alive and functioning, while another says some figures have speculated that he may have died or been left incapacitated after the alleged attack.
President Masoud Pezeshkian is said to have claimed a personal meeting with the supreme leader, although the asserted time and circumstances of that meeting were not established.
Iran, the United States and Israel had not publicly confirmed the specific assertions described here.