Rowhani, 64, officially assumes power as Iran's highest elected office at a ceremony on Saturday. He will receive the formal endorsement of the country's supreme leader Ayatollah Ali Khamenei following his surprise election triumph in June.
A former chief nuclear negotiator, Rowhani defeated his conservative rivals after gaining the key backing of both Rafsanjani and another ex-president, the reformist Mohammad Khatami.
He succeeds Mahmoud Ahmadinejad, whose eight-year presidency was marked by showdowns with Western powers over Iran's nuclear ambitions and severe economic pain at home, due to harsh international sanctions but also mismanagement.
After his swearing-in ceremony in parliament on Sunday, Rowhani will officially have two weeks to name a cabinet.
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But media reports, quoting sources close to him, say the mid-ranking Shiite cleric plans to reveal his proposed ministerial line-up the same day.
The conservative-dominated parliament will have 10 days to review the list and vote on the nominees.
Multiple lists of nominees have appeared, with many figures included in all of them. Mohammad Javad Zarif, Iran's former ambassador to the United Nations, is reportedly set to be named foreign minister.
Reports say Mohammad Forouzandeh, a former defence minister and current head of a powerful charity foundation, will be named as secretary of that council, replacing the incumbent and current top nuclear negotiator Saeed Jalili - who suffered a heavy defeat in the June presidential election.
Bijan Namdar Zanganeh, a technocrat who was oil minister for the eight years under Khatami, is tipped to return to the post. "If the lists reported by the media are confirmed, the cabinet will be filled with technocrats close to president Rafsanjani," a Tehran-based analyst told AFP.
According to the lists, many of the nominees are educated in the United States and Britain, Rowhani himself having earned a doctorate in constitutional law in Glasgow.