Both The New York Times and The Wall Street Journal reported that 3G Capital was among parties interested in pursuing a deal with Burger King. Neither publication named its sources.
Earlier in the day, The Wall Street Journal reported that the interested party was a different firm, 3i Group PLC.
When 3i denied its involvement, Burger King momentarily lost much of its hefty stock gains it made during the morning.
But by midday, the company's shares were on the climb again, gaining $2.48, or 15.1 percent, to $18.93 in trading.
A spokesman from Burger King declined to comment on the report, and a message left with 3G wasn't immediately returned.
In a research note, R.W. Baird analyst David E. Tarantino told investors that he was boosting his price target on the stock, expecting it to climb 15.5 percent in the next year. He'd previously expected a 9.4 percent gain.
But he said the likelihood of a buyout is speculative.
"Media reports ... seem plausible, but such a transaction remains highly uncertain," he wrote to investors, adding that the Miami company has healthy cash flows and an opportunity to increase productivity while expanding overseas.
Burger King is the second-largest hamburger chain after McDonald's Corp. But it's faring worse than its rival in a weak economy.
Burger King has 12,000 restaurants, already has connections to private equity firms. It was acquired by a group of firms in 2002 and went public in 2006. Those firms - TPG Capital, Bain Capital Partners and Goldman Sachs Funds - still own more than 30 percent of Burger King's outstanding shares.