There are three possible candidates, Ebrahim Raisi (kind of close to IRGC and the House of leadership, Hassan Rouhani (affiliated with Hashemi’s family and reformist party) and Sadegh Larijani (the head of the Larijani’s family).
(The image shows Ebrahim Raisi, the head of Astan Quds Razavi and a member of Assembly of Experts)
Ebrahim Raisi seems to be the candidate of choice ( presidency and leadership) for both IRGC and The House of leadership. In 2017 presidential election in Iran he lost to Rouhani but managed to get more than 900k votes in Tehran (!) and more than 15 million votes in total, which is not bad at all considering Iran had no president that runs only one term.
Here is why I think Raisi is the one even though he has not been involved in any significant political position, like Khamenei….
(The Image Above shows Ebrahim Raisi in Lebanese border with Israel)
One event made many really convinced, that Ebrahim Raisi would be the future supreme leader and that event is when Ebrahim Raisi visited Syria and Lebanon (at the end of January 2018) and met with many very high ranking Hezbollah commanders and religious figures (Sunni and Shia) near the Israeli -Lebonan border… in the politics of Shia Islam, this is called Oath of allegiance or [بیعت] in Farsi. He was sent there (probably by the supreme leader request) to ensure Iranian allies that he will be the real commander in chief in the future in Iran so to avoid any confusion.
(The image above is Ebrahim Raisi either in Lebonan or Syria but most likely Lebonan)
I think this event alone, proves that Ebrahim Raisi, in fact, will be the future leader in Iran. There might be a joined- attempts by others to grab this position but it is very unlikely that they can handle IRGC in any sustainable approach.
2) Hassan Rouhani
(The image above shows president Hassan Rouhani)
What they (IRGC + Leadership) are now having in mind is how to prevent the political party that is connected to Hashemi family to have any say in the future, because, this party has time and time again sent signals that pointed their rejection to some of the main ideas of the 1979 revolution ( Hashemi family means the entire of Rouhanis’s cabinet, all the reformists and some portion of the ministry of intelligence). This party and candidate has some advantages to all the other candidates and that is his popularity amongst the younger generation.
3) Sadegh Larijani
(The image above shows Sadegh Larijani)
Both IRGC and house of leadership but more IRGC don’t trust the Larijani’s family, who are in charge of parliament, the head of the judiciary, Chairman of Expediency Discernment Council and a member of the assembly of experts. But he (Sadegh Larijani) is a tough one to cross-over since he has all the requirements on paper to become the supreme leader. However, he is extremely unpopular amongst the people and IRGC in particular!
I’m kinda sure they don’t allow Larijani or Rouhani to become the future supreme leader because the pro-Islamic revolutionaries (by that I mean the ordinary people who strongly support the current supreme leader) will not be loyal to either of them. larijani is deeply hated by Ahmadinejad followers (who are also loyal to the supreme leader) and Rouhani is known as in the most critical terms you could find amongst the pro-revolutionaries.
I think Raisi’s last year visit to Syria and Lebonan proves that he, in fact, will be the future leader in Iran. There might be a joined- attempts by others to grab this position but it is very unlikely that they can handle IRGC in any sustainable way.
*Please have in mind, these are all just opinions and interpretations based on my grasp of news and events, certainly, I do not claim to know the absolute truth. These may very well be all untrue and inaccurate!*