Last month, British American Tobacco, which already owns 42 percent of Reynolds American, offered to buy the remaining shares of the maker of Camel and Newport cigarettes to create the world's biggest listed tobacco company.
"We thought it was a possibility, so it's not too surprising," Morningstar analyst Adam Fleck said in an email.
"Depending on how another offer from BATS could be structured, there's a bit of a circular argument here for the value of RAI," Fleck said.
The companies are still in talks and BAT is willing to increase the price slightly, Bloomberg said, citing people familiar with the matter.
Altria controls 51 percent of the U.S. market and Reynolds 34 percent.
Analysts estimate the Reynolds' acquisition would make the United States account for about 40 percent of BAT sales and 50 percent of its profits.
BAT's cash-and-stock offer would mark the return of the company to the lucrative and highly regulated U.S. market after a 12-year absence, making it the only tobacco giant with a leading presence in the American and international markets.
Some analysts have predicted that the deal could encourage current market leader Philip Morris International to reunite with its U.S. affiliate Altria, reversing a 2008 spin-off of the international business.
Both Reynolds American and BAT declined to comment.
Bloomberg was the first to report on Reynolds' rejection.
Reynolds American had a market capitalization of about $76 billion as of Monday's close of $53.05. The company's stock had risen nearly 15 percent this year.