The discussions put Allergan in direct competition with Japan's Takeda Pharmaceutical for the London-listed drugmaker.
Shire rebuffed Takeda on Thursday, turning down an offer worth around $61 billion. Shire said the offer of $66.15 per share in cash and stock "significantly undervalued the company, its growth prospects and pipeline."
Allergan said in a statement that it has not submitted an offer and that there is no certainty of a bid. The company is required by law to announce its intention to make an offer for Shire by May 17.
With additional reporting from Reuters.