Both drugmakers have approached Biogen regarding a possible deal, The Wall Street Journal reported, citing people familiar with the matter.
The paper said those sources said the discussions were informal and preliminary, and they may not result in a deal — in part because Biogen may not be interested. However, a source told CNBC that Allergan is unlikely to pursue the deal.
In mid-July, CEO George Scangos said he would leave Biogen in the coming months, once his replacement was found. That news sparked speculation that Scangos' departure could be a trigger for the biotech to be acquired.
"Obviously I can't comment on that," Scangos told CNBC on July 21. "That wouldn't make any logical sense to me that because I'm leaving, the company is in play. We all believe, the board believes, I believe, the future is bright for Biogen."
Scangos had been at Biogen for the past six years. In May, the company announced plans to spin off its hemophilia business, and it is in the midst of restructuring program, begun last October to cut costs and narrow its focus on core areas.
When contacted by CNBC, Biogen had no comment.
Merck spokeswoman Lainie Keller said, "We don't comment on speculation."
Allergan spokesman Mark Marmur also declined comment, saying, "Allergan does not comment on market rumor or speculation."
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— CNBC's Meg Tirrell contributed to this report.