The billionaire's investment would come in addition to the 1 percent stake held by David Tepper's Appaloosa Management. On Tuesday, Tepper said in a letter he is pushing the drugmaker to overhaul its management.
Shares of Allergan rose 2.6 percent in premarket trading Thursday.
"Allergan welcomes all investments in our company," the firm said in a statement. "We maintain an active dialogue with our shareholders and value their constructive input and ideas on delivering long-term value."
Icahn bought a big stake in Allergan in 2016 but sold out about a year later.