Both al-Jaafari, who heads the Islamic Dawa Party, and Hakim, who heads the Supreme Council for Islamic Revolution in Iraq (SCIRI), have close ties to Tehran.
SCIRIs military wing, the Badr Brigade, is believed to be behind several high-level assassinations and kidnappings in central and southern Iraq.
Zalmay Khalilzad, the American ambassador in Baghdad is drawing up a scenario to set aside the Hakim-al-Jaafari alliance from power in Iraq, the online journal Entekhab wrote.
The goal of this plan is to replace Ibrahim al-Jaafari with Ayad Allawi, the former Prime Minister, and empowering secular Shiites in the place of more religious Shiites, it said, adding that the plan had been drawn up prior to the election campaigns.
The government-run website reported that the plan was based on preserving the U.S.s enormous interests in Iraq and the Middle East.
The U.S. is hopeful that with such a plan, the result of the December legislative elections will be a victory for secular Shiites who are more in line with Americas policies in Iraq and the region.