Altria shares surged the most since October 2008 on the news, rising as much as 11%. Philip Morris declined as much as 7.6%, the most since December.
The companies broke apart more than a decade ago, bowing to pressure from US investors who wanted higher dividends and more share buybacks.
The move was also pitched as a way to set free faster-growing overseas operations while the US business was entangled in smoker lawsuits.
But times have changed. Altria has recently diversified its portfolio with investments in vaping and cannabis, giving the company more growth potential even as fewer people smoke cigarettes.
Some analysts and investors have argued for years that the companies should get back together, a move that would give Philip Morris more US exposure.
There has been speculation that the companies might get back together. On Monday, Wells Fargo published a research note that said a deal could make sense now, in part because Altria has a stake in the vaping company Juul.
Philip Morris had a market value of nearly $121 billion at the close of trading in New York on Monday, while Altria was worth about $88 billion.
A reunification would combine two of the most popular smoking alternative products: IQOS and Juul. Philip Morris has been ploughing billions of dollars in promoting IQOS, a heat-not-burn product used by millions consumers outside the US.
Altria meanwhile has invested $12.8 billion in e-cigarette upstart Juul Labs Inc., which has catapulted itself to the US industry leader in smoking alternatives in just a few years.
Altria also has been planning to start selling IQOS in the U.S. this year, testing out demand in the Atlanta area with a store opening next month.
Philip Morris said in a statement that no agreement has been formally reached and any deal would be subject to board, shareholder and regulatory approval. Altria also issued a statement confirming the talks.