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And this move is all about Iran positioning itself to become the major player in the Shi'ite regions of Iraq.
Iran has been sending surveillance drones over Iraq, and is providing the government-backed military with manpower and arms. There is also an Iranian intelligence unit that has been deployed in the region to intercept communications between the leadership of ISIS, the Sunni extremist group that's taken over much of Iraq's north and west.
But Iran's involvement goes beyond simply aiding a neighboring government. There are strategic underpinnings to what it's doing, which is where a figure like Chalabi could become important.
"Iran is likely to be playing somewhat of an overarching command role within the central Iraqi military apparatus, with an emphasis on maintaining cohesiveness in Baghdad and the Shia south and managing the reconstitution of Shia militias," Charles Lister, a visiting fellow at the Brookings Doha Center in Qatar, told the New York Times.
Although American officials have said Iranian forces are massed on the border with Iraq - ready to fight for Maliki if the Shi'ite south is in serious trouble - the Iranians might see the necessity of replacing Iraq's troublesome prime minister. Quite possibly the only government that isn't trying to have Maliki removed are the Russians, who claim a $4 billion defense contract is contingent on Maliki remaining in power.
If Maliki does go, there might not be a better choice for Tehran than Chalabi, who has been an ally of Iran dating back to the late-1970s Iranian Revolution.
"For Chalabi, Iran is the place where power and Shi'ism have come together in the form of the Islamic revolution. He is very loyal to Iran," Aram Roston, who wrote a book on Chalabi, told Mother Jones. "And of course during the Iran-Iraq war, Chalabi, who was an exile banker opposed to Saddam Hussein, rooted quite vocally for Iran instead of for his own country."
Just one year after the U.S. invaded Iraq, American special forces raided Chalabi's Baghdad home in an attempt to find information that he was leaking information to the Iranians. He would then become an ally of the Sadrists - Iraq's most hardcore Shi'ite sectarians and their Iranian patrons, as well as with the Shi'ites' supreme leader, Ayatollah Ali al-Sistani.
Iran has wanted to dominate the Shi'ite areas in Iraq since before the conclusion of the Iraq War in 2010. Chalabi could be Tehran's means of imposing its will on its fractious next door neighbor.