Mylan's cash and stock bid for its larger rival, which came in early last week, valued Actavis at $120 per share, the person said, asking not to be identified because the matter is not public.
The Mylan offer came shortly after Actavis halted discussions with Canadian drugmaker Valeant Pharmaceuticals International about selling itself for more than $13 billion, the person said.
Canonsburg, Pa.-based Mylan is no longer actively pursuing a deal after shares of Actavis rose significantly over the past week, to above its $120 per share offer, the person added.
Actavis shares ended Tuesday at $121.68 on the New York Stock Exchange, valuing the company at more than $15.5 billion. Mylan shares rose 3 percent to $30.10, making the company worth about $11.5 billion.
An Actavis spokesman and a Mylan spokeswoman declined to comment. News of Mylan's offer and its rejection by Actavis was first reported by Bloomberg.
Actavis said on Friday it is in preliminary talks to acquire specialty pharmaceutical company Warner Chilcott.