3G could not immediately be reached and a Burger King spokesman declined comment.
The second-biggest U.S. hamburger chain has underperformed rivals like McDonald's Corp as its key customer base of young men has been hit harder by unemployment in the past two years.
That group has suffered massive job losses in industries like construction and manufacturing.
The company, which has a market capitalization of about $2.3 billion, debuted as a public company in May 2006 with an initial share price of $17.
Shares were up 15 percent to $18.92 in midday trading.
Famed for its flame-broiled Whopper, Burger King had previously been owned by private equity firms, which still hold a stake in the company. TPG, Bain Capital and Goldman Sachs purchased Burger King from British beverage company Diageo in 2002 for about $1.5 billion.
One of the potential suitors, British private equity firm 3i Group Plc , distanced itself from a possible deal.
We can confirm that we are not in discussions with Burger King, a spokeswoman for 3i said.
Burger King last week 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. The company said it was unsure how costs for key ingredients like beef would impact the company.
Its shares hit a low of $16.30 in mid-August, but surged to $19.50 in premarket trading on Wednesday.
Private equity firms have become increasingly active and last month was the busiest August since 1999 in terms of the value of merger and acquisition deals struck.
In August, Blackstone Group struck a deal to buy power company Dynegy Inc for $543 million, or $4.7 billion including debt.
(Reporting by Megan Davies in New York, Simon Meads in London and Lisa Baertlein in Los Angeles; Additional reporting by Krishna N. Das in Bangalore and Ben Klayman in Detroit; Editing by Mike Nesbit, Dave Zimmerman and Gunna Dickson)