The opinion of the Shia community in Najaf is that Wilayat al-Faqih, https://en.wikipedia.org/wiki/Guardianship_of_the_Islamic_Jurist i.e. the Khomeini version of how to run a country with a supreme leader on the top of the heap is wrong.
Iran has several times tried to push Najaf/Karbala to change this and even tried to push for https://en.wikipedia.org/wiki/Mahmoud_Hashemi_Shahroudi as a replacement (He died 2018 only 70 years old)
According to an article in 2018 by the Kurdistan Conflict and Crisis Research Center there are some possible replacements: https://en.wikipedia.org/wiki/Muhammad_Saeed_al-Hakim ,
https://en.wikipedia.org/wiki/Bashir_al-Najafi
and https://en.wikipedia.org/wiki/Muhammad_al-Fayadh
http://www.kurdistanc.com/EN/details.aspx?jimare=1050
I have not investigated this enough to give an educated guess. But it is probably important to check who Sheikh Abdul Mahdi al-Karbalai, the spokesperson for Sistani is spending time with.
However, Iran's Supreme Leader Ayatollah Ali Khamenei has directed Iraqi leaders to shut down Iraq's protests, even if that means more violence.
and on November 21, Khamenei met in Tehran with Iraqi officials including Falih al-Fayadh, head of Iraq's Popular Mobilization Units (PMU); Hadi al-Amiri, head of the pro-Iran Badr Organization; and Mohammad Hashimi, head of the prime minister's office.
Mohammad Hashimi just resigned.
It is likely that more persons in Iran are listening to Sistani than to Khamenei, and the change of government in Iraq may increase the pressure in Iran.
The persons around Khamenei are probably very nervous today.