Deadline reports that the cable network is close to signing a deal to pick up the programme.
The Killing, based on the Danish show Forbrydelsen, examines the murder of a young girl and the police investigation which follows it.
The story is told from the perspective of the family, the suspects and the police team but focuses on lead detective Sarah (Mireille Enos).
Former True Blood star Michelle Forbes also stars in the pilot along with Billy Campbell, Brent Sexton, Kristin Lehman, Eric Ladin, Jamie Anne Allman and Joel Kinnaman.
AMC already airs Mad Men, Breaking Bad and Rubicon. It is currently developing the historical western Hell On Wheels and zombie drama The Walking Dead.