The deal would mark a fast and profitable exit for Starr, which bought MultiPlan for $4.4 billion in 2014.
Starr is run by Maurice "Hank" Greenberg, who set the firm up after exiting AIG, where he was CEO, in 2005.
Starr was AIG's biggest shareholder when the insurance giant was bailed out during the financial crisis. Greenberg famously tried to take the government to court for bailout, seeking up to $50 billion in damages.
The MultiPlan deal, which could still fall apart according the WSJ, would break the silence in the private equity space, where firms are sitting on mountains of cash but having a hard time finding bargains.
Private equity firms paid out $2 billion in fees to the investment banks advising them on deals in the first quarter, down 38% from 2015, and the lowest since the first three months of 2010.
"Low interest rates creates higher prices and higher prices are the enemy of wonderful returns," Blackstone CEO Steve Schwarzman told CNBC on Tuesday.
"So it makes it more difficult to set deals up. So you have to be very careful, do something clever and make enormous amount of value that historically investors are used to."
For the full story, head over to The Wall Street Journal.