If successful, they'd create the world's largest healthcare company, with a combined market cap of around $330 billion.
The deal would allow Pfizer to reincorporate in Ireland, where Allergan is domiciled, and taxes are lower.
It's a type of deal known as a tax inversion.
The merger would be just the latest in a string of deals that has let at least four different companies cut their tax bills by merging into what is now called Allergan.
Here's how that went:
- As Bloomberg's Zachary Mider notes, it all started with a small pharmaceutical called Galen, based in Northern Ireland and founded in 1968.
- By 2008, Mider notes, Galen had moved to Ireland and renamed itself Warner-Chilcott. It had a market cap of about $3.8 billion by late 2008.
- Then, in 2009, Warner-Chilcott bought Procter & Gamble's global pharmaceuticals business.
- In 2013, Warner-Chilcott was bought by Actavis, a New Jersey-based pharmaceutical. It moved its address to Ireland.
- Ireland-based Actavis bought another US firm, Forest Laboratories, in 2014.
- Then, earlier this year, Actavis bought California-based Allergan and took its name.
- Now, Ireland-based Allergan is looking to merge with Pfizer.
Ireland's corporate tax rate is only 12.5%.
Meanwhile, Pfizer is currently paying an effective tax rate of 25%, according to Bloomberg analysts Elizabeth Krutoholow and Curt Wanek. So moving to Ireland could cut the company's tax bill in half.
It's no secret that Pfizer has been looking to do an inversion. CEO Ian Read has repeatedly said that tax is a competitive challenge for companies like his in the US, and even tried to pull off an inversion in 2014 by merging with UK-based AstraZeneca.
Drugmakers are also keen to move overseas to avoid having to pay taxes on foreign profits. Once redomiciled in Ireland, Pfizer could bring some of its cash back - to fund everything from dividends to acquisitions, without paying the higher US rates.
Tax inversions were common in the 1990s but really became a hot topic in the past two years. Last September, the US Treasury introduced a regulation to make inversions harder to pull off.
But if the Allergan-Pfizer deal goes through and is structured as an inversion, it would be the largest such deal on record.