Burger King Holdings Inc
The second-biggest U.S. hamburger chain has underperformed rivals like McDonald's
That group has suffered massive job losses in industries like construction and manufacturing.
The company, which has a market capitalisation of about $2.3 billion (1.4 billion pounds), has been public since May 2006.
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 drinks company Diageo
One of the potential suitors, British private equity firm 3i Group Plc
We can confirm that we are not in discussions with Burger King, a spokeswoman for 3i said.
Burger King could not immediately be reached for comment.
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 (10.54 pounds) in mid-August, but surged to $19.50 (12.60 pounds) 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 (350 million pounds), or $4.7 billion (3.0 billion pounds) including debt.
(Reporting by Megan Davies and Simon Meads; Additional reporting by Krishna N. Das in Bangalore and Ben Klayman in Detroit; Editing by Mike Nesbit, Dave Zimmerman)