Shares of Burger King, the No. 2 U.S. hamburger chain, surged 23 percent to $23.20 after the report. They had gained nearly 15 percent on Wednesday after news of a potential deal first emerged.
Burger King has lagged larger rival McDonald's Corp (MCD.N) and other fast food chains as its key customer base takes a deeper hit from persistently high unemployment rates.
Last week, the company forecast weak demand during its new fiscal year due to the U.S. economy's slow pace of recovery and government austerity programs in several European countries.
Analysts said it was an opportune time for the company to go private, just over four years after a group of private equity firms took it public in May 2006 at an initial share price of $17.
Burger King and 3G officials were not immediately available for comment.