In separate, printed statements, both companies said that they were in "preliminary friendly discussions."
A merger could enable Viagra maker Pfizer, the world's second-biggest drugmaker by revenue, to surpass Switzerland's Novartis AG and add to its extensive portfolio of vaccines and drugs for cancer, pain, erectile dysfunction and other conditions.
Allergan said there's no certainty that the talks with Pfizer Inc. will lead to a deal.
Pfizer, which has been damaged by waves of generic drugs that have entered the market and cut into sales of one-time blockbuster drugs like cholesterol fighter Lipitor, has been making large acquisitions to boost revenue and cut costs.
A deal for Allergan, based in Dublin, would allow for additional growth and Pfizer may pursue an "inversion," a tax-saving maneuver in which a U.S. company reincorporates in a country with a friendlier tax rate.
Inversions have become a hot political topic, raising the ire of lawmakers in Washington.
Last week, billionaire Carl Icahn said that he was setting up a $150 million super PAC bent on revising U.S. corporate tax law and ending the practice of inversions.
Pfizer, based in New York, said in its statement that it won't comment "on speculation regarding the terms of a potential transaction.
"Any further announcement will be made if and when appropriate," Pfizer said.
After being suspended in early trading, shares of Allergan jumped almost 9 percent. Shares of Pfizer edged slightly lower.