The healthcare sector has seen an unprecedented wave of deals since early 2014, from large drugmakers buying up smaller rivals, to consolidation among makers of generic medicines and tie-ups between insurers.
A bid for Allergan, which has a market value of $113 billion, would be Pfizer's second recent attempt to acquire a big rival, following its unsuccessful courtship last year of Anglo-Swedish pharmaceuticals group AstraZeneca.
Combining Allergan and Pfizer, which is worth $219 billion, would create the world's largest healthcare group with a market value of around $330 billion, ahead of Johnson & Johnson on $278 billion.
A Pfizer spokesman said it "does not comment on market rumor and speculation." Allergan also declined to comment.
The potential for lowering Pfizer's tax bill by switching its headquarters from the United States to the United Kingdom was touted by Chief Executive Officer Ian Read as a key reason for the proposed AstraZeneca deal.
A takeover of Allergan could offer similar advantages given that the Botox-maker is based in lower-tax Dublin. A U.S. attempt to crack down on such tax avoidance deals led to the collapse of AbbVie's bid to buy Shire, but it is unclear whether those rule changes would preclude potential tax advantages from a Pfizer-Allergan deal.
"When you're the size of Pfizer, an acquisition like this may be the only choice you have in order to be able to move the needle for sequential growth...so the question now becomes, if not this, what, and if not now, when?" said WBB Securities' analyst Stephen Brozak.
Pfizer, the largest U.S. drugmaker, has also been suggested as a possible acquirer of GlaxoSmithKline and Shire, and shares in these two companies fell 1.5 and 1.8 percent on Thursday morning in London.
Allergan would give Pfizer, whose revenues are expected to slide 3.3 percent this year, a boost in top-line growth. The Botox-maker's revenue is seen increasing 39 percent this year, according to Thomson Reuters I/B/E/S estimates.
Bernstein analyst Tim Anderson said Allergan was a good fit and Pfizer might feel now was the right time to do a deal, given a recent market correction that has made Allergan look cheap.
The merger talks are in early stages, and may not yield an agreement, while other details are unclear, The Wall Street Journalsaid.
The Financial Times, which reported the talks later, described the talks as preliminary. Reuters was not immediately able to confirm the reports.
Allergan became the third-largest generic drugmaker in the United States after combining with Actavis in March.
Its chief executive, Brent Saunders, has been eager to do deals, having first orchestrated the sale of Forest Laboratories Inc, where he was initially CEO, to Actavis, then using the latter to seal the $66 billion purchase of Allergan.
Following the Actavis tie-up, Allergan sold its generic drugs business to Israel's Teva Pharmaceutical Industries in July for $40.5 billion in cash and stock. And Saunders said after that he hoped to use those
proceeds to do another large, "transformational" merger.
In its first full quarter after the Actavis deal, Allergan reported second-quarter revenue of $5.76 billion, led by $632 million in sales of wrinkle blocker Botox. Other top-selling drugs include dry eye treatment Restasis and Alzheimer's drug Namenda.
Pfizer recently reported third-quarter revenue of $12.1 billion, including $1.58 billion for its Prevnar pneumococcal vaccines and $947 million for pain drug Lyrica.
While Pfizer wanted to buy AstraZeneca in part to boost Pfizer's pipeline of cancer drugs, a deal with Allergan would involve dermatology drugs and generics.