Greenberg is a partner and the media/cable/satellite and consumer sector head at Paulson & Co. Friday is her last day, the report said.
Her new fund will focus on long/short equity.
She would be among a few female hedge fund CEOs.
Some of her successful event-driven equity investments at Paulson include Cablevision, Family Dollar, Time Warner Cable, Sara Lee / Hillshire Brands, WhiteWave, AMC Networks and Comcast, according to her LinkedIn.
In November, she pitched Charter Communications as a long idea on behalf of Paulson & Co. at the Robin Hood Investor Conference. She predicted that the share price could rise to $294 in 24 months and her bull case was $325.
Greenberg joined Paulson & Co. in July 2009. Before that, she worked at Goldman Sachs in the bank's special situations group as a vice president focused on distressed credit for the media, telecom and consumer sectors, according to her LinkedIn. She has also worked at Chilton Investment Company as a long/short equity analyst and Francisco Partners as a private equity associate.
Greenberg has been named one of Ernst & Young's "50 Leading Women in Hedge Funds."
She graduated summa cum laude from UPenn's Wharton with a bachelor's degree in economics. She holds an MBA from Stanford University.