The source said one potentially interested party was 3i Group.
Burger King, which has a market capitalization of about $2.3 billion, has been public since May 2006.
It had previously been own by private equity, which still holds a stake in the company. TPG, Bain Capital and Goldman Sachs had owned Burger King after buying it from British drinks company Diageo in 2002 for about $1.5 billion.
The Wall Street Journal reported Burger King has been in talks with private equity firms in recent weeks about a possible sale.
3i declined to comment when contacted by CNBC.